📐 Shop math and conversions

Fraction, decimal and millimetre chart

1 inch = 25.4 mm exactly. To go from a fraction to a decimal, divide the top number by the bottom number. To get mm, multiply decimal inches by 25.4.

Unit conversions

• Length: 1 in = 25.4 mm; 1 ft = 0.3048 m; 1 m = 3.2808 ft; 1 mile = 1.6093 km
• Pressure: 1 psi = 6.8948 kPa; 1 bar = 100 kPa = 14.504 psi; 1 MPa = 145.04 psi; 1 inHg = 3.3864 kPa
• Torque: 1 lbf·ft = 1.3558 N·m; 1 N·m = 0.7376 lbf·ft; 1 lbf·in = 0.11298 N·m; 12 lbf·in = 1 lbf·ft
• Temperature: °F = °C × 9/5 + 32; °C = (°F − 32) × 5/9
• Mass and force: 1 lb = 0.4536 kg; 1 kg = 2.2046 lb; 1 lbf = 4.4482 N
• Volume: 1 US gal = 3.7854 L; 1 imperial gal = 4.5461 L; 1 ft³ = 28.317 L; 1 L = 61.024 in³
• Power: 1 hp = 745.7 W; 1 kW = 1.341 hp

Pythagoras and right-angle trig

In a right triangle with legs a and b and hypotenuse c (the long side opposite the 90° corner):

• c = √(a² + b²), and a = √(c² − b²)
• sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent
• The two acute angles always add up to 90°.
• The 3-4-5 rule (or any multiple, like 6-8-10 or 9-12-15) checks a square corner.

Area and volume

• Rectangle: A = L × W
• Triangle: A = ½ × base × height
• Circle: A = π × r² = 0.7854 × D²; circumference = π × D
• Box: V = L × W × H
• Cylinder: V = 0.7854 × D² × L
• Cone: V = ⅓ × π × r² × h
• Sphere: V = 4/3 × π × r³
• Keep the units the same: inches in, cubic inches out. 231 in³ = 1 US gal; 1,000,000 mm³ = 1 L.

Percent and ratio

• Percent = part ÷ whole × 100
• Percent change = (new − old) ÷ old × 100
• A ratio like 3:1 means 3 parts of one thing for every 1 part of the other, or 4 parts in total.
• To mix by ratio, divide the total by the number of parts, then multiply by each side's parts.