Case Hardening (Carburizing)
Purpose: Create an extremely hard, wear-resistant surface while maintaining a tough, ductile core.
Process: Heat low-carbon steel (0.15–0.25% C) in a carbon-rich environment at 1,600–1,700°F, allowing carbon to diffuse into the surface. Then quench to harden the carbon-enriched case.
Result: Surface hardness of 55–63 HRC with core hardness of 160–350 BHN (depending on alloy). The case depth ranges from a few thousandths to over 0.100 inch.
the practitioner's choice for her pinion: Casehardening steels with their extremely hard, fine-grained case and comparatively soft, ductile core are generally used when resistance to wear is desired. The casehardened pinion runs against a gear treated to a Brinell hardness at which the teeth may be cut after treating — an excellent combination for high-ratio applications.
Nitriding
Purpose: Extremely hard surface with minimal distortion.
Process: Heat steel containing aluminum, chromium, or molybdenum to approximately 950–1,050°F in an atmosphere of ammonia gas for extended periods (20–90 hours). Nitrogen diffuses into the surface and forms extremely hard nitrides.
Result: Surface hardness of 90–94 HRA (Rockwell A) with core hardness of 300–370 BHN. No quenching required — the parts are furnace cooled. Distortion is minimal because temperatures are well below the transformation range.
Critical caution: Care must be exercised in running nitrided gears together to avoid crazing of case-hardened surfaces.
Surface Hardening (Flame and Induction)
Purpose: Selective hardening of specific areas without treating the entire part.
Flame Hardening: A gas flame rapidly heats the surface above the critical temperature, followed immediately by quenching.
Induction Hardening: High-frequency alternating current in a coil generates eddy currents in the steel surface, heating it rapidly. Then quench.
Laser Hardening: A focused laser beam heats the surface. The absorbed energy, converted to heat, raises the temperature for as long as the beam remains in one place. Dwell time controls case depth. Typical hardening rate: 130 cm²/min (20 in²/min) for a 1 mm case depth in 4140 steel.
Materials applicability for laser hardening:
- Good candidates: Medium- and high-carbon steels, tool steels, low-alloy steels, cast irons with fine-carbide dispersion
- Marginal: Annealed carbon steels, spheroidized steels, mild carbon steels (0.2% C)
- Not hardenable: Low-carbon steels (<0.1% C), austenitic stainless steels, nonferrous alloys
Steels for Gears: The Complete Heat Treatment Decision Matrix
This is where theory meets the shop floor. the practitioner — and every gear engineer — needs this reference.
Case-Hardening Steels:
| Material | Rc (Surface) | Core BHN | Treatment | Application |
|---|---|---|---|---|
| AISI 1020 / 1116 | 55–60 | 160–230 | Carburize, harden, temper 350°F | Wear-resistant gears. Normalized material easily machined. Ductile core |
| AISI 4130 / 4140 | 50–55 | 270–370 | Harden, temper 900°F, nitride | Greater wear resistance than thru-hardened. Shallow case, tough core |
| AISI 4615 / 4620 / 8615 | 55–60 | 170–260 | Carburize, harden, temper 350°F | High fatigue resistance and strength. 86xx series has better machinability |
| AISI 8620 | 55–60 | 200–300 | Carburize, harden, temper 350°F | The 20-point steels are used for coarser teeth |
| AISI 9310 | 58–63 | 250–350 | Carburize, harden, temper 300°F | Aerospace gears. High loading, high pitch-line velocity |
| Nitralloy N/135 Mod | 90–94 HRA | 300–370 | Harden, temper 1,200°F, nitride | Cannot tolerate carburizing distortion. High-temperature operation |
Through-Hardening Steels:
| Material | HRC Range | Treatment | Application |
|---|---|---|---|
| AISI 1045 / 1140 | 24–40 | Harden and temper to required hardness | Medium/large gears. Moderate strength. Consistent sections |
| AISI 4140 | 24–40 | Harden (oil quench), temper | High strength and wear resistance. Moderate sections |
| AISI 4340 | 24–40 | Harden (oil quench), temper | High shock loading resistance. Heavy sections |
Carbon Steels for Gears — Chemical Composition (AGMA):
| Heat Treatment Class | Carbon | Manganese | Phosphorus | Sulfur |
|---|---|---|---|---|
| C — Case-hardened | 0.15–0.25% | 0.40–0.70% | 0.045% max | 0.055% max |
| N — Untreated | 0.25–0.50% | 0.50–0.80% | 0.045% max | 0.055% max |
| H — Hardened | 0.40–0.50% | 0.40–0.70% | 0.045% max | 0.055% max |
The Effect of Alloying Elements on Steel
Understanding why certain alloys are chosen requires knowing what each element does:
Nickel: Increases hardness and strength with little sacrifice of ductility. Greater hardness penetration. Lowers critical points, producing less distortion due to lower quenching temperature. Nickel steels carburize more slowly but with less grain growth.
Chromium: Increases hardness and strength more than nickel, with greater loss of ductility. Refines grain structure. Imparts deeper hardness penetration. Increases wear resistance.
Molybdenum: Increases toughness and resistance to softening at elevated temperatures. Reduces temper brittleness. Enhances hardenability.
Vanadium: Grain refiner. Increases strength and toughness. Improves resistance to softening during tempering.
Manganese: Increases hardenability and tensile strength. Enhances the effects of sulfur by forming manganese sulfide (improving machinability).
Making the pinion harder than the gear to equalize wear: Beneficial results are obtained by making the pinion harder than the gear. The pinion, having fewer teeth, does more work per tooth. The differential in hardness serves to equalize the rate of wear. The harder pinion teeth correct errors in the gear teeth to some extent by initial wear, then seem to burnish the gear teeth and increase their ability to withstand wear through cold-working of the surface.
Surface Treatment and Coating Standards: Protection That Lasts
Beyond heat treatment, surfaces are protected by coatings and platings that resist corrosion, reduce friction, and extend service life. Here are the critical standards you need to know.
Metallic Coatings
| Coating | Specification | Typical Thickness | Key Properties |
|---|---|---|---|
| Cadmium | QQ-P-416F | 0.0002–0.0005 in. | Corrosion resistance. Types I (as-plated), II (chromate), III (phosphate) |
| Chrome (Hard) | QQ-C-320B | 0.0001–0.002 in. | Excellent hardness, wear, and erosion resistance |
| Nickel | QQ-N-290A | 0.0004–0.002 in. | 150–500 Vickers. Corrosion resistance. Low thermal expansion |
| Zinc | ASTM-B633 | Per class | Corrosion resistance for iron/steel. Types I–IV |
| Gold | MIL-G-45204C | 0.00002–0.0015 in. | 90–201+ Knoop depending on grade |
| Tin | MIL-T-10727C | 0.0001–0.0025 in. | Gray-white. Good solderability. Prevents galling |
| Palladium | MIL-P-45209B | 0.00005 in. | Good wear, corrosion resistance, conductivity |
| Vacuum Cadmium | MIL-C-8837B | 0.0002–0.0005 in. | Corrosion resistance without hydrogen embrittlement |
Anodic Coatings (Aluminum)
| Type | Specification | Thickness | Application |
|---|---|---|---|
| Type I & IB | MIL-A-8625F | 0.00002–0.0007 in. | Fatigue-critical components. Chromic acid process |
| Type IC | MIL-A-8625F | 0.00002–0.0007 in. | Non-chromate alternative. Mineral/mixed acid |
| Type II | MIL-A-8625F | 0.0007–0.0010 in. | Standard sulfuric acid anodize |
| Type III (Hard Anodize) | MIL-A-8625F | 0.0005–0.0045 in. | Very hard ceramic-type coating. Excellent abrasion resistance |
Chemical and Conversion Coatings
| Coating | Specification | Key Properties |
|---|---|---|
| Chemical Film | MIL-C-5541E | Corrosion prevention on aluminum. Class 1A for unpainted; Class 3 for electrical contacts |
| Black Oxide | MIL-C-13924C | Decorative black for ferrous metals. Minimal corrosion protection. Used where dimensional change cannot be tolerated |
| Black Chrome | MIL-C-14538C | Non-reflective, ~0.0002 in. thick. Abrasion, heat, and corrosion resistant |
| Passivation | QQ-P-35C | Improves corrosion resistance of stainless steels (200, 300, 400 series) |
Critical Rules for Plating High-Strength Steel
- Steel parts ≥ 220 ksi tensile (40 HRC): Brightening agents in cadmium plating solution are prohibited
- Stress relief before plating: All steel parts ≥ 1,000 MPa ultimate tensile must be baked at minimum 190°C for 3+ hours before cleaning and plating
- Hydrogen embrittlement relief: All electroplated parts ≥ 1,200 MPa must be baked at 190°C for 3+ hours within 4 hours after plating
- Cadmium: Service temperature must not reach 450°F
- High-strength steels (>1,700 MPa): Shall NOT be electroplated with zinc
Nondestructive Testing (NDT): Inspecting Without Destroying
The final chapter of the practitioner's story. After his inspector caught the over-hardened rebar, the question became: how do you verify internal quality without cutting the part open?
Nondestructive testing examines a component — usually for surface or internal cracks, nonhomogeneities, thickness, or structural soundness — without impairing its use.
NDT Methods at a Glance
| Symbol | Method | What It Detects | Best For |
|---|---|---|---|
| VT | Visual | Surface defects, alignment, dimensions | First-pass inspection of all components |
| PT | Penetrant (Dye) | Surface-breaking cracks and porosity | Non-magnetic materials, welds, castings |
| MT | Magnetic Particle | Surface and near-surface defects | Ferromagnetic materials only |
| RT | Radiographic (X-ray/Gamma) | Internal voids, inclusions, cracks | Castings, welds, thick sections |
| UT | Ultrasonic | Internal flaws, thickness measurement | All metals, composites, thickness gauging |
| ET | Eddy Current | Surface cracks, conductivity changes, coating thickness | Tubing, aircraft skins, conductive materials |
| AET | Acoustic Emission | Active crack growth, leaks, deformation | Pressure vessels, structures under load |
| LT | Leak Testing | Through-wall defects in pressure boundaries | Piping, tanks, sealed assemblies |
| NRT | Neutron Radiographic | Internal features in dense materials | Explosive assemblies, nuclear components |
| PRT | Proof Testing | Structural adequacy under load | Pressure vessels, lifting equipment |
NDT Symbol System (ANSI/AWS 2.4-79)
Testing symbols follow the same conventions as welding symbols:
- Arrow connects the reference line to the part being tested
- Arrow side — tests indicated by the symbol below the reference line (toward the reader)
- Other side — tests indicated by the symbol above the reference line
- Both sides — symbols on both sides of the reference line
- Test-all-around — circular symbol indicates testing around an entire joint
- Number of tests — shown in parentheses: (N)
- Length of section — shown to the right of the basic test symbol
Ultrasonic Bolt Load Measurement
A particularly elegant application of ultrasonic testing: a sound pulse generated at one end of a bolt travels its length, bounces off the far end, and returns in a measured time period. The travel time depends on bolt length, material speed of sound, and stress level. By comparing travel times in loaded versus unstressed conditions, the system computes stress, load, or elongation.
Where:
- δ_B = bolt elongation
- θ = turn angle of the nut (degrees)
- l = lead of the thread helix
This connects NDT directly to the turn-of-nut method of bolt preloading — a critical quality control technique in structural steel and pressure vessel work.
Strength Grade Systems: Reading the Marks on Your Fasteners
SAE/ASTM Grade System (Inch Fasteners)
The head markings on a bolt tell its grade. The grade determines minimum tensile strength, yield strength, and proof load:
| Grade | Identifier | Size Range | Min. Proof (ksi) | Min. Tensile (ksi) | Min. Yield (ksi) | Material / Treatment |
|---|---|---|---|---|---|---|
| SAE 1 | No mark | 1/4–1½ | 33 | 60 | 36 | Low/medium carbon |
| SAE 2 | No mark | 1/4–3/4 | 55 | 74 | 57 | Low/medium carbon |
| SAE 5 | 3 radial lines | 1/4–1 | 85 | 120 | 92 | Medium carbon, Q&T |
| SAE 7 | 6 radial lines | 1/4–1½ | 105 | 133 | 115 | Medium-carbon alloy, Q&T |
| SAE 8 | 6 radial lines | 1/4–1½ | 120 | 150 | 130 | Medium-carbon alloy, Q&T |
| ASTM A325 | "A325" | 1/2–1½ | 85–74 | 120–105 | 92–81 | Medium carbon or martensite, Q&T |
| ASTM A490 | "A490" | 1/2–1½ | 120 | 150 | 130 | Alloy steel, Q&T |
ISO Metric Grade System
The metric system uses a two-number designation. The first figure is 1/10 of the minimum tensile strength in kgf/mm². The second figure is 1/10 of the yield-to-tensile ratio percentage.
Example — Grade 8.8:
- First figure (8): Minimum tensile strength = 80 kgf/mm²
- Second figure (8): Yield/tensile ratio = 80%, so yield stress = 64 kgf/mm²
| Grade | Min. Tensile (kgf/mm²) | Min. Yield or R₀.₂ (kgf/mm²) |
|---|---|---|
| 4.6 | 40 | 24 |
| 4.8 | 40 | 32 |
| 5.6 | 50 | 30 |
| 5.8 | 50 | 40 |
| 6.6 | 60 | 36 |
| 6.8 | 60 | 48 |
| 8.8 | 80 | 64 |
| 10.9 | 100 | 90 |
| 12.9 | 120 | 108 |
| 14.9 | 140 | 126 |
Nut Grade System: The grade number is 1/10 of the proof load stress in kgf/mm². The proof load stress corresponds to the minimum tensile strength of the highest grade bolt the nut can be used with.
Detecting counterfeit fasteners: Fasteners that carry grade markings but do not meet the standards are counterfeit. They may break unexpectedly at smaller loads. The only sure way to verify is to test. Typical laboratory checks include testing hardness, elongation, and ultimate loading, plus chemical analysis.
Hard-Facing Materials: When the Surface Must Be Tougher Than the Core
When the practitioner's colleague the practitioner was specifying wear-resistant surfaces for mining equipment, she turned to hard-facing materials. These are deposited by welding, spraying, or cladding to provide wear resistance, corrosion resistance, or both.
Hard-Facing Selection Guide
| Material | Form | As-Deposited Hardness | Hot Hardness | Impact Resistance | Key Applications |
|---|---|---|---|---|---|
| High-Speed Steel (RFe5/EFe5) | Rod/Electrode | 55–60 HRC | 47 HRC at 1,100°F | Medium (as-deposited); good (tempered) | Cutting tools, shear blades, forming dies |
| Austenitic Manganese Steel (EFeMn) | Electrode | 170–230 BHN (work-hardens to 450–550) | Brittle above 500–600°F | High | Rock crushers, railway crossings |
| Austenitic High-Chromium Iron (RFeCr-A/EFeCr-A) | Rod/Electrode | 51–62 HRC | 43 HRC at 900°F | Light only | Agricultural machinery, sand-blasting equipment |
| Cobalt-Base Alloys (RCoCr/ECoCr) | Rod/Electrode | CoCr-A: 38–47; CoCr-B: 45–49; CoCr-C: 48–58 HRC | Outstanding above 1,200°F | Moderate to low | Exhaust valves, valve trim, pump shafts |
| Copper-Base Alloys (RCuAl/ECuSn/ECuZn) | Rod/Electrode | CuAl: 90–250 BHN; CuSn: 80–200 BHN | Decreases rapidly | Moderate | Bearings, guides, seal surfaces |
| Nickel-Chromium-Boron (RNiCr/ENiCr) | Rod/Electrode | NiCr-A: 35–40; NiCr-B: 45–50; NiCr-C: 56–62 HRC | NiCr-C rod: 55–40 HRC (600–1,000°F) | Light to moderate | Seal rings, valves, cams, screw conveyors |
Key Properties of NiCr Alloys at Elevated Temperatures
| Alloy | Temperature Range | Hardness (HRC) | Conditions |
|---|---|---|---|
| NiCr-A (rod) | 600–1,000°F | 34–24 | Instantaneous to 3-minute loading |
| NiCr-B (rod) | 600–1,000°F | 46–37 | Instantaneous to 3-minute loading |
| NiCr-C (rod) | 600–1,000°F | 55–40 | Instantaneous to 3-minute loading |
NiCr deposits are completely resistant to atmospheric, steam, salt water, and salt spray corrosion and to milder acids and many common corrosive chemicals. Their use above 1,750°F is not recommended because fusion may begin near this temperature.
Chromium Plating for Tools and Gages
Chromium plating extends tool life dramatically on nearly all classes of materials — brass, bronze, copper, nickel, aluminum, cast iron, steel, plastics, and composites. Increased cutting life has been demonstrated with chromium-plated drills, taps, reamers, files, broaches, and saws.
Thickness range: 0.0001 to 0.001 or 0.002 inch. Thicker platings are used to build up undersize tools such as taps and reamers.
For gages: Chromium-plated plug and ring gages wear significantly longer. When worn, the chromium may be removed and the gage replated and reground to size — extending gage life by multiples.
The Resolution: the practitioner's Takeaway — And Yours
At 3:42 AM, the practitioner's inspector had his answer. The reinforcement bars were over-hardened — strong but potentially brittle. They were pulled for retesting, the heat treatment lot was quarantined, and a full metallurgical investigation traced the issue to a furnace thermocouple that had drifted 85°F high, pushing quench temperatures past specification.
The thermocouple was reading in Celsius. The spec was written in Fahrenheit. Nobody caught the mismatch until the hardness numbers screamed "something is wrong."
A unit error. A measurement gap. The same kind of gap that this entire guide was built to close.
Your Quick-Reference Decision Framework
When you encounter any material specification, property, or test result, follow this systematic approach:
Step 1 — Identify the measurement system. Is the drawing in metric or English? SI or traditional? Never assume.
Step 2 — Verify the unit. Is that stress value in psi, ksi, MPa, or kgf/mm²? A number without its unit is a number without meaning.
Step 3 — Convert with precision. Use verified conversion factors from authoritative sources. Never round intermediate steps.
Step 4 — Understand what the number means. A hardness of 60 HRC tells you about wear resistance — but also tells you about brittleness, machinability, and grinding difficulty.
Step 5 — Connect properties to treatment. Every mechanical property is the result of composition PLUS processing. Two parts from the same steel can perform completely differently based on heat treatment.
Step 6 — Verify through testing. Specifications on paper are only as good as the testing that verifies them. Know which NDT method applies, understand its capabilities and limitations, and never skip the inspection step.
Your Next Step
Save this guide. Put it where you can reach it — in your toolbox, your office, your digital library.
Then ask yourself this question: When was the last time you verified the units on a specification before acting on it?
If the answer gives you pause, you have already learned the most important lesson this guide has to offer.
Measurement is not about numbers. It is about meaning. And meaning is what keeps structures standing, machines running, and people safe.
What measurement conversion or material property question has tripped you up in the past? What reference table do you wish you always had within reach? Share your experience — because the next engineer who reads this might be facing the exact same challenge right now.
The Complete Engineering Reference
The $4.7 Million Bolt That Cracked Because Someone Confused Kilograms with Pounds
the practitioner had been a quality inspector at a heavy equipment manufacturer for eleven years. He was meticulous. He was trusted. He was wrong—and it nearly killed two people on a construction site in Southeast Asia.
The problem wasn't negligence. It was a unit conversion error buried three layers deep in a materials specification document. A heat-treated alloy steel bolt rated at 120,000 pounds per square inch of tensile strength was substituted with a metric-specified fastener rated at 80 kgf/mm². On paper, the numbers looked close enough. In reality, the metric bolt was rated for roughly 113,800 psi—a 5% shortfall that, under cyclic loading, caused catastrophic fatigue failure at 14 months of service.
The crane boom dropped. The insurance claim hit seven figures. And the practitioner spent the next year of his career rebuilding trust—by becoming the most obsessive student of measuring units, material properties, heat treatment, and testing his company had ever seen.
This guide is the manual the practitioner wished he'd had on day one.
Whether you're a machinist converting microinches to micrometers at the bench, an engineer specifying heat treatment for gear steels, or a project manager who needs to understand why your team argues about Rockwell C versus Brinell hardness numbers—this is your permanent reference.
The Measurement Systems That Run the World
Why Two Systems Still Exist (And Why It Matters More Than You Think)
Before the practitioner could fix anything, he had to confront a truth that seasoned engineers often take for granted: the world runs on two incompatible measurement systems, and the friction between them kills people, destroys equipment, and costs industries staggering sums every year.
The U.S. customary system (often loosely called the "English" or "Imperial" system) and the International System of Units (SI, from the French Système International d'Unités) are not just different scales. They represent fundamentally different philosophies of organizing physical reality.
Understanding both systems—and the conversions between them—is not optional for anyone working with materials, manufacturing, or engineering.
The U.S. Customary System: A Patchwork of History
The U.S. customary system evolved organically over centuries. Its units carry the fingerprints of agrarian life, maritime trade, and medieval commerce. The system is not decimal-based, which means conversions between units within the same category require memorization or lookup.
Linear Measure
| Unit | Equivalents |
|---|---|
| 1 mile | 5,280 feet = 1,760 yards = 8 furlongs |
| 1 yard | 3 feet = 36 inches |
| 1 foot | 12 inches |
| 1 inch | Subdivided into fractional parts (1/2, 1/4, 1/8, 1/16, 1/32, 1/64) |
For precision work, inches are expressed as decimals. The conversion from fractional to decimal equivalents is foundational:
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/64 | 0.015625 | 17/32 | 0.53125 |
| 1/32 | 0.03125 | 9/16 | 0.5625 |
| 1/16 | 0.0625 | 5/8 | 0.625 |
| 1/8 | 0.125 | 11/16 | 0.6875 |
| 3/16 | 0.1875 | 3/4 | 0.750 |
| 1/4 | 0.250 | 13/16 | 0.8125 |
| 5/16 | 0.3125 | 7/8 | 0.875 |
| 3/8 | 0.375 | 15/16 | 0.9375 |
| 7/16 | 0.4375 | 1 | 1.000 |
| 1/2 | 0.500 | — | — |
Critical insight: In machining, a callout of "0.375 inches" is far more useful than "3/8 inch" because CNC machines, micrometers, and coordinate measuring machines all work in decimal notation. Get comfortable converting between the two instantly.
Surveyor's and Nautical Measures
These specialized linear measures persist in land surveying and maritime navigation:
- 1 chain = 66 feet = 100 links (each link = 7.92 inches)
- 1 furlong = 10 chains = 220 yards
- 1 nautical mile = 6,076.115 feet = 1.1508 statute miles
- 1 knot = 1 nautical mile per hour
Square Measure
| Unit | Equivalents |
|---|---|
| 1 square mile | 640 acres = 6,400 square chains |
| 1 acre | 10 square chains = 4,840 square yards = 43,560 square feet |
| 1 square yard | 9 square feet |
| 1 square foot | 144 square inches |
| 1 circular mil | Area of a circle 0.001 inch in diameter |
| 1 square inch | 1,273,239 circular mils |
Why circular mils matter: Electrical engineers use circular mils to specify wire cross-sectional area. It simplifies calculations because the area of a circular conductor is simply the diameter in thousandths of an inch, squared.
Cubic Measure
| Unit | Equivalents |
|---|---|
| 1 cubic yard | 27 cubic feet |
| 1 cubic foot | 1,728 cubic inches |
| 1 cord of wood | 4 × 4 × 8 feet = 128 cubic feet |
| 1 perch of masonry | 16½ × 1½ × 1 feet = 24¾ cubic feet |
Weight Systems
Here is where the U.S. customary system becomes genuinely treacherous. Three different weight systems coexist:
Avoirdupois (Commercial) Weight:
- 1 pound = 16 ounces = 7,000 grains
- 1 ounce = 16 drachms = 437.5 grains
- 1 short ton = 2,000 pounds
- 1 long ton = 2,240 pounds
Troy Weight (for precious metals):
- 1 pound = 12 ounces = 5,760 grains
- 1 ounce = 20 pennyweights = 480 grains
- 1 pennyweight = 24 grains
- 1 carat = 3.086 grains
Apothecaries' Weight:
- Uses the same pound and ounce as Troy weight
- 1 ounce = 8 drachms; 1 drachm = 3 scruples; 1 scruple = 20 grains
The trap: 1 grain Troy = 1 grain avoirdupois = 1 grain apothecaries'. But 1 ounce Troy (480 grains) ≠ 1 ounce avoirdupois (437.5 grains). And 1 pound Troy (5,760 grains) ≠ 1 pound avoirdupois (7,000 grains). the practitioner's colleague once priced gold using avoirdupois ounces instead of Troy ounces. The error was 9.7%.
Liquid and Dry Measure
| Liquid Measure | Equivalents |
|---|---|
| 1 U.S. gallon | 231 cubic inches = 0.1337 cubic feet |
| 1 quart | 2 pints = 8 gills |
| 1 British Imperial gallon | 277.42 cubic inches = 1.2009 U.S. gallons |
| Dry Measure | Equivalents |
|---|---|
| 1 bushel | 4 pecks = 32 quarts = 64 pints |
| 1 cubic foot | 0.8036 struck bushel |
Measures of Pressure
| Unit | Equivalents |
|---|---|
| 1 pound per square inch (psi) | 2.042 inches of mercury (at 62°F) |
| 1 pound per square inch | 2.309 feet of water (at 62°F) |
| 1 atmosphere | 14.696 psi = 29.921 inches Hg |
| 1 foot of water (at 62°F) | 62.355 lb/ft² = 0.4335 psi |
| 1 inch of mercury (at 62°F) | 1.132 feet of water = 0.4912 psi |
The Metric System: From CGS to MKS to SI
The metric system didn't arrive fully formed. Its evolution is a story of increasing coherence—and it's essential to understand the stages because legacy metric units still appear in older engineering documents.
The CGS System (Centimeter-Gram-Second)
The original scientific metric system, which defined:
- Unit of force: 1 dyne = the force needed to accelerate 1 gram at 1 cm/s²
- Unit of work: 1 erg = 1 dyne-centimeter
- Unit of power: 1 watt = 10,000,000 ergs per second
- Gravitational acceleration (at Paris) = 981 cm/s²
The MKS and MKSA Systems
In 1902, the practitioner proposed the MKS (meter-kilogram-second) system. In 1935, the International Electrotechnical Commission (IEC) accepted his recommendation to link this system with electromagnetic units by adopting the ampere. By 1950, the MKSA system was born.
A parallel gravitational system—the "technical system"—used the meter, the kilogram-force, and the second. But because the kilogram-force depends on local gravitational acceleration (which varies around the earth), this system was inherently imprecise. A standard value of was adopted by international agreement, but the fundamental problem remained.
The International System of Units (SI)
In 1960, the Conférence Générale des Poids et Mesures (CGPM) formally established the SI system. In 1971, the 14th CGPM added the mole as a seventh base unit.
The Seven SI Base Units:
| Physical Quantity | Unit Name | Symbol | Definition |
|---|---|---|---|
| Length | meter | m | Distance traveled by light in vacuum in 1/299,792,458 of a second |
| Mass | kilogram | kg | Mass of the international prototype (historically); now defined via Planck constant |
| Time | second | s | Duration of 9,192,631,770 periods of radiation from cesium-133 ground state transition |
| Electric Current | ampere | A | Current producing a force of 2 × 10⁻⁷ N/m between two infinite parallel conductors 1 m apart |
| Temperature | kelvin | K | 1/273.16 of the thermodynamic temperature of the triple point of water |
| Amount of Substance | mole | mol | Amount of substance containing as many entities as atoms in 0.012 kg of carbon-12 |
| Luminous Intensity | candela | cd | Luminous intensity in a given direction of a source emitting monochromatic radiation |
SI Derived Units with Special Names
| Quantity | Unit | Symbol | Derivation |
|---|---|---|---|
| Force | newton | N | kg·m/s² |
| Pressure/Stress | pascal | Pa | N/m² |
| Energy/Work | joule | J | N·m = kg·m²/s² |
| Power | watt | W | J/s = kg·m²/s³ |
| Electric Potential | volt | V | W/A |
| Electric Resistance | ohm | Ω | V/A |
| Electric Capacitance | farad | F | C/V |
| Magnetic Flux | weber | Wb | V·s |
| Inductance | henry | H | V·s/A |
| Luminous Flux | lumen | lm | cd·sr |
| Illumination | lux | lx | lm/m² |
| Frequency | hertz | Hz | cycles/second |
| Magnetic Flux Density | tesla | T | Wb/m² |
SI Units with Complex (Unnamed) Derivations
| Quantity | SI Unit |
|---|---|
| Area | square meter (m²) |
| Volume | cubic meter (m³) |
| Density | kilogram per cubic meter (kg/m³) |
| Velocity | meter per second (m/s) |
| Acceleration | meter per second squared (m/s²) |
| Angular Velocity | radian per second (rad/s) |
| Dynamic Viscosity | newton second per meter squared (N·s/m²) |
| Kinematic Viscosity | meter squared per second (m²/s) |
| Surface Tension | newton per meter (N/m) |
| Thermal Conductivity | watt per meter kelvin (W/m·K) |
| Electric Field Strength | volt per meter (V/m) |
| Luminance | candela per square meter (cd/m²) |
Why the Newton Matters
This is the single most important conceptual shift when moving from traditional metric or U.S. customary systems to SI.
In older systems, engineers habitually used weight units (kilograms-force, pounds-force) as force units. The newton eliminates this confusion:
1 newton = the force that gives a mass of 1 kilogram an acceleration of 1 meter per second squared. It is independent of gravitational acceleration, which means:
- The factor disappears from dynamics calculations
- In statics formulas where weight (not mass) is the input, reappears: a mass of kilograms equals a force of newtons, where
- Horsepower is not used in SI. It is replaced entirely by the watt and its multiples (kilowatt, megawatt).
