§1Two systems, one exact bridge
Since the 1959 international agreement, the yard and pound are defined in metric terms — so the systems are not two independent standards but one, joined by exact numbers.
From the inch follow the foot (12 in = 0.3048 m), yard and mile; from the pound follow the ounce, ton, and — once gravity enters — the pound-force. Because the anchors are exact, the only reason any factor below is rounded is legibility; carry more digits whenever the tolerance demands. A caution the tables make explicit: the US and imperial systems agree on length but diverge on volume (the two gallons differ by about 20 %), so “gallon” without its nationality is a genuine trap.
Contents§2Length
Every length factor is the exact inch, scaled.
| From | To | Multiply by |
|---|---|---|
| inch (in) | mm | 25.4 |
| foot (ft) | m | 0.3048 |
| yard (yd) | m | 0.9144 |
| mile | km | 1.609 34 |
| mm | in | 0.039 37 |
| metre (m) | ft | 3.280 84 |
| kilometre (km) | mile | 0.621 371 |
| The inch, foot and yard are exact; the reverse factors are their reciprocals, rounded here for reading. | ||
§3Area and volume
Area factors are the length factor squared; volume, cubed — which is where the numbers grow surprising, and where the two gallons part ways.
| From | To | Multiply by |
|---|---|---|
| square inch (in²) | mm² | 645.16 |
| square foot (ft²) | m² | 0.092 903 |
| acre | m² | 4046.86 |
| acre | hectare (ha) | 0.404 686 |
| cubic inch (in³) | cm³ (mL) | 16.3871 |
| US gallon | litre (L) | 3.785 41 |
| imperial gallon | litre (L) | 4.546 09 |
| The US gallon is defined as exactly 231 in³; the imperial gallon is larger, so a “20 mpg” US figure and a “20 mpg” UK figure are different economies. One hectare is 10 000 m² by definition — a 100 m square. | ||
§4Mass and force
Mass converts through the exact pound; force adds one step — standard gravity, 9.806 65 m/s² — because a pound-force is the weight of a pound mass.
| From | To | Multiply by |
|---|---|---|
| pound-mass (lb) | kg | 0.453 592 |
| ounce (oz) | g | 28.3495 |
| short ton (2000 lb) | tonne (t) | 0.907 185 |
| kilogram (kg) | lb | 2.204 62 |
| pound-force (lbf) | N | 4.448 22 |
| newton (N) | lbf | 0.224 809 |
| Mass and force are different quantities: the kilogram measures mass, the newton force. The pound-force is the weight of one pound-mass under standard gravity. | ||
The distinction the metric system keeps clean and the customary one blurs: the kilogram is mass, the newton is force, and they are never the same quantity. A pound does duty as both (pound-mass and pound-force), which is exactly why unit slips happen at the boundary — always resolve which is meant before converting.
Contents§5Pressure and stress
Pressure is force over area, so its factor is the pound-force over the square inch: 1 psi = 6894.76 Pa.
| From | To | Multiply by |
|---|---|---|
| psi (lbf/in²) | kPa | 6.894 76 |
| psi | MPa | 0.006 895 |
| bar | psi | 14.5038 |
| atmosphere (atm) | kPa | 101.325 |
| megapascal (MPa) | psi | 145.038 |
| 1 bar = 100 kPa exactly; 1 standard atmosphere = 101.325 kPa. Stress converts identically — steel yield of 250 MPa is about 36 300 psi. | ||
A system rated 3000 psi: 3000 × 6894.76 Pa = 20 684 272 Pa = 20.7 MPa — squarely in the range of the hydraulic cylinder barrel sized on the Plates, Shells and Cylinders page. Reading the other way, 1 MPa is 145 psi, so a 200 MPa yield strength is about 29 000 psi.
§6Temperature
Temperature is the one conversion that is not a single multiplier — the scales have different zeros, so an offset is involved.
Water freezes at 32 °F = 0 °C and boils at 212 °F = 100 °C. The metrology reference temperature 68 °F is exactly 20 °C = 293.15 K — the 20 °C at which every dimension in this Library is defined (the Measuring Instruments page). And the scales cross once: −40 °F = −40 °C, a useful check that the formula is the right way round.
A subtlety worth keeping: a temperature difference converts without the offset — a change of 9 °F is a change of 5 °C — which is why the thermal-expansion coefficient on the Strength of Materials page (11.7 µm per metre per °C) needs only the ratio, not the +32.
Contents§7Torque, power and speed
Compound mechanical units convert by combining the factors already established — torque is force times length, power is energy per time, speed is length per time.
| From | To | Multiply by |
|---|---|---|
| pound-force foot (lbf·ft) | N·m | 1.355 82 |
| newton metre (N·m) | lbf·ft | 0.737 562 |
| horsepower (hp) | kW | 0.745 700 |
| mile per hour (mph) | km/h | 1.609 34 |
| mile per hour (mph) | m/s | 0.447 04 |
| knot | km/h | 1.852 |
| Horsepower here is the mechanical (550 ft·lbf/s) value, 745.7 W; the metric horsepower (PS) differs at 735.5 W — another unit to name before converting. | ||
A bolt specified at 75 lbf·ft is 75 × 1.35582 = 101.7 N·m — the torque a mid-size spanner delivers. And 60 mph is 60 × 1.60934 = 96.6 km/h (26.82 m/s) — the factor 1.609 being the mile in kilometres, straight from §2.
§8Converting safely
Conversion errors are avoidable with a few habits that cost nothing.
Carry the units through the arithmetic as algebra — write the factor as a fraction equal to one (25.4 mm / 1 in) and cancel, so a wrong-way conversion cancels visibly rather than hiding. Respect significant figures: a dimension known to ±1 mm gains nothing from eight decimal places of conversion — round the result to the precision of the input, not the precision of the factor. Know which factors are exact (the inch, foot, pound, US gallon) and which are rounded (psi to pascals, horsepower to watts), so you know where the uncertainty enters. And name the system for the ambiguous units — US or imperial gallon, short or long ton, mechanical or metric horsepower — because those differ by enough to matter. When a converted number will drive a real part, verify it the way every figure in this Library is verified: independently, in the open.
Contents§9Quick reference
The working core of the page on one card rack.
Anchors (exact)
1 in = 25.4 mm
1 lb = 0.453 592 37 kg
Length
ft ×0.3048 · mile ×1.609
m ×3.281 ft · km ×0.621 mi
Force / pressure
lbf ×4.448 N · psi ×6.895 kPa
1 MPa = 145 psi
Temperature
°C = (°F−32)×5/9
68 °F = 20 °C · −40 crosses
Motion
lbf·ft ×1.356 N·m · hp ×0.746 kW
mph ×1.609 km/h