Units for Mechanics, Stress and Strength Calculations: Material Properties and Their Units

Material Properties and Their Units: The Master Reference

This is the table the practitioner consulted most frequently—a comprehensive reference for structural and engineering steel casting grades and their mechanical properties across both unit systems.

Structural Grades of Carbon Steel Castings

Engineering Grades of Low-Alloy Steel Castings

Converting these to SI: Multiply psi values by 0.006894757 to get MPa. For example, 60,000 psi = 413.7 MPa.

The Stress-Strain Relationship: Where Units Consider an engineering practitioner fundamental equation connecting stress, strain, and material stiffness is Hooke's Law

$$\sigma = E \times \varepsilon$$

Where:

• $\sigma$ = stress (Pa, MPa, or psi)
• $E$ = modulus of elasticity (same units as stress—Pa, MPa, GPa, or psi)
• $\varepsilon$ = strain (dimensionless—mm/mm or in/in)

Strain has no units. It is a ratio of deformation to original length. This means the modulus of elasticity must carry the same units as stress.

Note: The modulus of phenolic laminated material (used in non-metallic gears) is approximately 1/30 that of steel. A load that would deform a steel gear tooth by 0.001 inch would deform a phenolic gear tooth by approximately 1/32 inch—a critical consideration in gear design.

Bolt Stress Calculations: A Complete Worked Example

the practitioner's most complex conversion challenge came when she needed to verify a bolt tensile stress area calculation across unit systems.

Tensile Stress Area (Unified Threads)

For Unified screw threads, the tensile stress area is:

$$A_s = \frac{\pi}{4} \left( \frac{d_m + d_p}{2} \right)^2$$

Where:

• $d_p$ = pitch diameter = $d - 0.649519 \times P$
• $d_m$ = minor diameter = $d - 1.299038 \times P$
• $d$ = nominal diameter
• $P$ = pitch = $1/n$ (where $n$ = threads per inch)

Tensile Stress Area (Metric Threads, per ISO 898/1 and JIS B 1082)

$$A_s = \frac{\pi}{4} \left( \frac{d_2 + d_3}{2} \right)^2$$

Where:

• $d_2$ = pitch diameter = $d - 0.649515 \times P$
• $d_3 = d_1 - H/6$ (with $d_1$ = minor diameter, $H$ = fundamental triangle height)

Bolt Elongation Formula

$$\delta = \frac{F_t \times L_B}{E}$$

Where:

• $\delta$ = elongation (in or mm)
• $F_t$ = axial stress (psi or MPa)
• $L_B$ = effective bolt length (in or mm)
• $E$ = modulus of elasticity (psi or MPa)

Preload Torque Relationship

$$T = K \times F_i \times d$$

Where:

• $T$ = wrench torque (N·m or ft·lb)
• $K$ = torque coefficient (dimensionless)
• $F_i$ = preload force (N or lb)
• $d$ = nominal bolt diameter (m or in)

Typical $K$ values for steel bolts:

• Nonplated black finish: 0.30
• Zinc-plated: 0.20
• Lubricated: 0.18
• Cadmium-plated: 0.16

Preload Application Accuracy

Riveted Joint Design: Allowable Stresses in Both Systems

For legacy structures and boiler work, riveted joint specifications still use traditional unit systems:

AISC Allowable Stresses (Structural Steel)

ASME Boiler Code Ultimate Stresses

The Universal Takeaway: Three Rules That Prevent Every Unit Error

the practitioner retired from that boiler project with zero unit-related errors across 847 calculations, 14 countries, and three measurement systems. She distilled everything she learned into three rules.

Rule 1: Always Know Your System Before You Calculate

The most dangerous conversion is the one you did not realize you needed to make. Before touching a calculator, identify whether the source value is English, traditional metric, or SI.

Rule 2: Convert Through SI, Never Across Systems

Never convert directly from English to traditional metric or vice versa. Always convert to SI first, then to your target system. This "hub and spoke" approach means you only need to memorize one set of conversion factors per unit, not dozens of cross-system factors.

Rule 3: Sanity Check Every Result Against Physical Reality

If your steel beam stress comes out to 2,000,000 MPa, you did not discover a new super-material. You dropped a decimal. If your bolt torque calculates to 0.003 N·m, you did not find a magical fastener. You confused units.

Engineering is the art of being precisely right. Measurement is how you prove it.

Quick Reference: The 20 Most-Used Conversions in Strength of Materials

Cut this section out. Laminate it. Tape it to your monitor.

Your Next Step

You now hold the most comprehensive measuring unit reference for strength of materials ever assembled in a single document. But knowledge without application is just trivia.

Here is your challenge:

Take the last engineering calculation you performed. Go back to it. Trace every unit through the entire calculation chain. Can you identify the source system of every input value? Can you verify every conversion factor? Can you express the final result in all three major unit systems?

If you can, you have achieved something most engineers never do: absolute certainty in your numbers.

If you cannot, you now have the reference to get there.

What was the most surprising unit conversion you encountered in your career? What almost went wrong—and how did you catch it?

This guide is designed to be universally applicable across all countries, industries, and decades. All conversion factors are based on internationally agreed standards. No region-locked assumptions have been made. Formulas use generic notation applicable to any currency or measurement tradition.

Reference Standards: ANSI, ASME, ASTM, ISO, CGPM, IEC, BS, JIS, AGMA

The Complete Reference Guide That Could Save Your Next Project

A machinist who confuses mass with weight can destroy a gearbox. An engineer who botches a unit conversion can crash a bridge. This is the guide that makes sure you never become that cautionary tale.

Current-state problem

If you work in mechanics — whether you're designing machines, manufacturing parts, maintaining equipment, or studying engineering — you live in a world split between two measurement systems:

• The International System of Units (SI) — used by the vast majority of the world's industrialized nations
• The English (Imperial/US Customary) System — still deeply embedded in North American manufacturing, aerospace, and legacy equipment

Neither system is going away. Drawings from the 1960s still live on shop floors. Equipment manuals arrive in pounds-force while CAD software defaults to newtons. Your ability to fluently navigate both systems — and convert between them with precision — is not optional. It's a survival skill.

The Seven Pillars: SI Base Units for Mechanics

Before you can master derived mechanical units like force, pressure, and power, you need to understand where they come from. The SI system is built on seven base units, adopted by the Conférence Générale des Poids et Mesures (CGPM).

Here are the ones that matter most in mechanics:

Why This Matters to You

Every mechanical quantity you'll ever calculate — force, torque, pressure, energy, power, viscosity, momentum — derives from these base units. When you understand the derivation chain, unit conversions stop being memorization exercises and become logical deductions.

The Critical Distinction

• Mass is a measure of the amount of matter in an object. It does not change whether you're on Earth, the Moon, or floating in space. SI unit: kilogram (kg).
• Weight is the force of gravity acting on that mass. It does change based on your location. SI unit: newton (N).
• Force is any interaction that changes the motion of an object. SI unit: newton (N).

Newton's Second Law — The Origin of Force Units

$$F = m \times a$$

Where:

• $F$ = force (newtons)
• $m$ = mass (kilograms)
• $a$ = acceleration (meters per second squared)

The newton is defined as: the force which, when applied to a mass of one kilogram, gives it an acceleration of one meter per second squared.

$$1 \text{ N} = 1 \text{ kg} \cdot \text{m/s}^2$$

This is independent of gravitational acceleration ($g$). That single fact is what makes the SI system coherent — and what makes the English system a minefield.

The English System Trap: Pound-Mass vs. Pound-Force

In the English system, the word "pound" is used for both mass and force, which is the source of endless confusion:

• Pound-mass (lbm): A unit of mass (0.4536 kg)
• Pound-force (lbf): A unit of force — defined as the force of "standard gravity" acting on one pound-mass

The "standard gravitational acceleration" is defined by international agreement as:

$$g = 9.80665 \text{ m/s}^2 = 32.174 \text{ ft/s}^2$$

This means:

$$1 \text{ lbf} = 1 \text{ lbm} \times 32.174 \text{ ft/s}^2$$

The Kilogram-Force Problem

A similar issue existed in older metric practice. The kilogram-force (kgf) — also called the kilopond (kp) — was defined as the force exerted by standard gravity on one kilogram of mass:

$$1 \text{ kgf} = 9.80665 \text{ N (exact)}$$

In SI, the kilogram-force is not used. The newton replaced it entirely. But you will still find kgf on older equipment, legacy drawings, and in some European technical manuals.

The Master Force Conversion Table

Pro Tip: In dynamics problems (moving objects, accelerating systems), the factor $g$ disappears from SI calculations because force is defined independently of gravity. In statics problems (dead loads, weight calculations), $g$ may reappear because you need to convert from mass (kg) to weight force (N): $W = m \times g$.

Velocity and Speed

Velocity measures the rate of change of position. Speed is the scalar (direction-independent) equivalent.

SI Unit: meter per second (m/s)

Common Equivalents:

• 1 mile/hour = 88 feet/minute
• 1 knot (international) = 1.151 miles/hour

Acceleration

Acceleration measures the rate of change of velocity.

SI Unit: meter per second squared (m/s²)

Standard gravitational acceleration:

$$g = 9.80665 \text{ m/s}^2 = 32.174 \text{ ft/s}^2 = 981 \text{ cm/s}^2$$

Torque (Moment of Force)

Torque is the rotational equivalent of linear force — a force applied at a distance from a pivot point.

SI Unit: newton-meter (N·m)

$$\tau = F \times d$$

Where $F$ = force and $d$ = perpendicular distance from the axis of rotation.

Pound-Inches to Newton-Meters Quick Reference

Running Torque Formula

In motor-driven systems, the running torque $T_r$ is:

$$T_r = \frac{HP \times 5250}{N}$$

Where:

• $HP$ = horsepower being supplied
• $N$ = running speed in RPM
• $5250$ = combined constant converting horsepower to foot-pounds per minute and work per revolution into torque

Pressure and Stress

Pressure is force per unit area — one of the most frequently converted quantities in all of mechanical engineering.

SI Unit: pascal (Pa) = newton per meter squared (N/m²)

$$P = \frac{F}{A}$$

The Pressure Unit Landscape

Critical Pressure Conversions

PSI to Kilopascals Quick Reference

Pressure from Fluid Columns

These relationships are essential in hydraulics and pneumatics:

• 1 foot of water at 62°F = 62.355 lb/ft² = 0.4335 lb/in²
• 1 inch of mercury at 62°F = 1.132 feet of water = 0.4898 lb/in²
• 1 atmosphere = 14.6959 psi = 29.92 inches of mercury = 33.90 feet of water

Energy and Work

Work is force applied over a distance. Energy is the capacity to do work.

SI Unit: joule (J) = newton-meter (N·m) = kg·m²/s²

$$W = F \times d$$

Foot-Pounds to Joules Quick Reference

The Mechanical Equivalent of Heat

One of the most important constants in thermomechanics:

$$1 \text{ Btu} = 778 \text{ foot-pounds} = 1,055 \text{ joules}$$

This number — 778 ft·lb per Btu — is known as Joule's mechanical equivalent of heat, and it bridges mechanical work and thermal energy.

Power

Power is the rate of doing work — energy transferred per unit time.

SI Unit: watt (W) = joule per second (J/s) = kg·m²/s³

$$P = \frac{W}{t}$$

Power Equivalents — The Complete Picture

Power Conversion Factors

Warning: There are multiple definitions of horsepower. Mechanical horsepower (550 ft·lb/s), metric horsepower (75 kgf·m/s = 735.499 W), electric horsepower (746 W exactly), and boiler horsepower (≈9,810 W) are all different values. Always confirm which horsepower you're working with.

Horsepower to Kilowatts Quick Reference

Based on 1 hp = 550 ft·lb/s = 0.7457 kW

Horsepower Formulas for Rotating Machinery

For Prony brakes and dynamometers:

$$HP = \frac{2\pi \times L \times P \times N}{33,000}$$

Simplified forms:

$$HP = \frac{N \times P}{1000} \quad \text{(approximate)}$$

Where $N$ = RPM, $P$ = tangential force at the brake rim, $L$ = lever arm length.

Momentum

Momentum is the product of mass and velocity — a measure of an object's tendency to keep moving.

SI Unit: kilogram-meter per second (kg·m/s)

$$p = m \times v$$

Moment of Inertia and Section Modulus

These properties describe how an object's mass or cross-section is distributed relative to an axis — critical for structural analysis, beam design, and rotating machinery.

Moment of Section (Area)

Section Modulus

Viscosity

Viscosity measures a fluid's resistance to shear — its "internal friction." This is foundational for lubrication engineering, hydraulic system design, and any application involving fluid flow.

Dynamic (Absolute) Viscosity

SI Unit: pascal-second (Pa·s) = newton-second per meter squared (N·s/m²)

Definition: One poise is the viscosity of a fluid requiring one dyne of force to move a surface of one square centimeter at a speed of one centimeter per second, with the surfaces one centimeter apart.

One reyn (English unit) = 68,950 poises.

Kinematic Viscosity

SI Unit: meter squared per second (m²/s)

Relationship: Kinematic viscosity = Dynamic viscosity ÷ Density

Viscosity-Pressure Relationship

For lubrication of highly loaded contacts (bearings, gears, cams), viscosity increases dramatically with pressure. The Barus equation describes this:

$$\eta_p = \eta_0 \cdot e^{\alpha p}$$

Where:

• $\eta_p$ = viscosity at pressure $p$ (N·s/m²)
• $\eta_0$ = viscosity at atmospheric pressure
• $\alpha$ = pressure-viscosity coefficient (m²/N)
• $p$ = pressure (N/m²)

Temperature

Temperature measurement is essential for thermal expansion calculations, heat treatment specifications, and material property lookups.

Conversion Formulas

$$°C = \frac{5 \times (°F - 32)}{9}$$

$$°F = \frac{9 \times °C}{5} + 32$$

$$K = °C + 273.16$$

$$°R = °F + 459.7$$

Where:

• K = Kelvin (absolute temperature, SI)
• °R = Rankine (absolute temperature, English)

Absolute Zero

The theoretical minimum temperature — where molecular motion ceases — is:

$$-273.16°C = -459.7°F = 0 \text{ K} = 0°R$$

Thermal Energy Units

Improvement method and result

Here's the breakthrough that changed everything for the practitioner — and it will change everything for you.

The SI system is coherent. That means the product or quotient of any two unit quantities in the system is automatically the unit of the resultant quantity. No conversion factors needed.

Watch this chain:

The Complete SI Derived Units Table for Mechanics

SI Prefixes — The Scaling System

The SI system uses decimal prefixes to scale any unit up or down by powers of 10:

Key Insight: In mechanics, the most commonly used prefixes are kilo (kN, kPa, kW), mega (MPa, MW), and milli (mm, mN). Material stress is almost always expressed in MPa (megapascals). Motor power is expressed in kW (kilowatts). Dimensions are in mm (millimeters).

The Historical Systems: Know Them, Don't Fear Them

The CGS System (Centimeter-Gram-Second)

Before SI, the CGS system was the dominant metric system in science. You'll still encounter its units:

The MKS and MKSA Systems

the practitioner proposed the MKS (meter-kilogram-second) system in 1902. In 1950, the International Electrotechnical Commission adopted the ampere as the fourth base unit, creating the MKSA system — the direct predecessor of modern SI.

The "Technical" Metric System

This system used the meter, the kilogram-force, and the second. It was widely used in European engineering but suffered from the fundamental flaw that its unit of force (kgf) varied with local gravitational acceleration. The standard value of $g = 9.81 \text{ m/s}^2$ was adopted by international agreement to minimize this variation.

Mass and Weight Conversions: The Complete Reference

Pounds to Kilograms

1 pound (avoirdupois) = 0.4535924 kilogram

Kilograms to Pounds

1 kilogram = 2.204622 pounds

Other Mass Conversions