All Unit Conversions
Formula Guide

A conversion factor is a multiplier that transforms one unit into another:

  • Linear: target = source \u00d7 factor
  • Non-linear: temperature uses addition too
  • Factors are ratios: 1 m = 3.28084 ft \u2192 factor = 3.28084

7 SI base units:

  • Meter (m) \u2014 length
  • Kilogram (kg) \u2014 mass
  • Second (s) \u2014 time
  • Ampere (A) \u2014 electric current
  • Kelvin (K) \u2014 temperature
  • Mole (mol) \u2014 amount
  • Candela (cd) \u2014 luminous intensity
  • Identify source and target units
  • Find the conversion factor between them
  • Multiply (or apply the formula for temperature)
  • Check: does the result make sense?
  • For chain conversions, multiply factors together

Unit Conversion Formulas & Equations

Understand the mathematics behind unit conversions. Each formula below shows the exact equation used to convert between units, along with a worked example. Whether you are a student learning dimensional analysis or an engineer double-checking a conversion, these formulas provide the mathematical foundation.

How factors are sourced, how the library is updated, and how IEEE 754 rounding is treated are documented on the About page.

Converters for these formulas

Use the published pair calculators that match the equations on this page.

Temperature Conversion Formulas

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Celsius to Fahrenheit

F = C × 9/5 + 32

Example: 25°C = 25 × 9/5 + 32 = 77°F

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Fahrenheit to Celsius

C = (F - 32) × 5/9

Example: 77°F = (77 - 32) × 5/9 = 25°C

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Celsius to Kelvin

K = C + 273.15

Example: 25°C = 25 + 273.15 = 298.15 K

Kelvin to Celsius

C = K - 273.15

Example: 300 K = 300 - 273.15 = 26.85°C

Fahrenheit to Kelvin

K = (F - 32) × 5/9 + 273.15

Example: 212°F = (212 - 32) × 5/9 + 273.15 = 373.15 K

Length Conversion Formulas

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Meters to Feet

ft = m × 3.28084

Example: 10 m = 10 × 3.28084 = 32.81 ft

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Feet to Meters

m = ft × 0.3048

Example: 100 ft = 100 × 0.3048 = 30.48 m

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Miles to Kilometers

km = mi × 1.60934

Example: 5 mi = 5 × 1.60934 = 8.05 km

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Inches to Centimeters

cm = in × 2.54

Example: 12 in = 12 × 2.54 = 30.48 cm

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Weight & Mass Conversion Formulas

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Kilograms to Pounds

lb = kg × 2.20462

Example: 70 kg = 70 × 2.20462 = 154.32 lb

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Pounds to Kilograms

kg = lb × 0.45359

Example: 150 lb = 150 × 0.45359 = 68.04 kg

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Ounces to Grams

g = oz × 28.3495

Example: 8 oz = 8 × 28.3495 = 226.80 g

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Volume Conversion Formulas

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Liters to US Gallons

gal = L × 0.264172

Example: 10 L = 10 × 0.264172 = 2.64 gal

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US Cups to Milliliters

mL = cups × 236.588

Example: 2 cups = 2 × 236.588 = 473.18 mL

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US Fluid Ounces to Milliliters

mL = fl oz × 29.5735

Example: 8 fl oz = 8 × 29.5735 = 236.59 mL

Speed Conversion Formulas

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mph to km/h

km/h = mph × 1.60934

Example: 60 mph = 60 × 1.60934 = 96.56 km/h

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km/h to m/s

m/s = km/h × 0.27778

Example: 100 km/h = 100 × 0.27778 = 27.78 m/s

Knots to km/h

km/h = knots × 1.852

Example: 30 knots = 30 × 1.852 = 55.56 km/h

Pressure Conversion Formulas

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Pascal to Bar

bar = Pa × 0.00001

Example: 101325 Pa = 101325 × 0.00001 = 1.013 bar

PSI to Pascal

Pa = PSI × 6894.76

Example: 14.7 PSI = 14.7 × 6894.76 = 101325 Pa

ATM to Pascal

Pa = atm × 101325

Example: 1 atm = 1 × 101325 = 101325 Pa

Energy Conversion Formulas

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Joules to Calories

cal = J × 0.239006

Example: 1000 J = 1000 × 0.239006 = 239.01 cal

kWh to Joules

J = kWh × 3,600,000

Example: 1 kWh = 1 × 3,600,000 = 3,600,000 J

BTU to Joules

J = BTU × 1055.06

Example: 100 BTU = 100 × 1055.06 = 105,506 J

Power Conversion Formulas

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Watts to Horsepower

hp = W × 0.001341

Example: 746 W = 746 × 0.001341 = 1.0 hp

Horsepower to Watts

W = hp × 745.7

Example: 2 hp = 2 × 745.7 = 1491.4 W

kW to Horsepower

hp = kW × 1.341

Example: 100 kW = 100 × 1.341 = 134.1 hp

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The Mathematics Behind Conversion

Linear Conversions

Most unit conversions are linear \u2014 you simply multiply by a conversion factor. For example, to convert meters to feet, multiply by 3.28084. The general formula is: target = source \u00d7 (toFactor / fromFactor)

Non-Linear Conversions

Temperature is the main exception. Because Celsius, Fahrenheit, and Kelvin have different zero points, conversion requires both multiplication and addition. For example: \u00b0F = \u00b0C \u00d7 9/5 + 32

Dimensional Analysis

For complex conversions, use dimensional analysis: write each conversion as a fraction where the units cancel. For example, converting miles per hour to meters per second: mph \u00d7 (1609.34 m/mi) \u00d7 (1 hr/3600 s) = m/s

All Category Formulas

Visit each category page for complete formula references and interactive calculators.

LengthWeight & MassTemperatureAreaVolumeSpeedEnergyPowerForcePressureElectricityMagnetismLightSoundRadiationHeatFluidEngineeringAngleNumbersTypographyData TransferDate-TimeCaseCulinaryFuel ConsumptionPrefixHealth & Fitness

Formula FAQs

Common questions about conversion formulas and equations.

What is a conversion factor?

A conversion factor is a ratio that expresses how many of one unit equals another unit. For example, 1 meter = 3.28084 feet, so the conversion factor from meters to feet is 3.28084. To convert, multiply your value by the conversion factor. Most conversions are simple multiplication, except temperature which uses addition and subtraction.

Why is temperature conversion different from other units?

Temperature scales have different zero points. Celsius and Fahrenheit don't share a common zero — 0°C equals 32°F, not 0°F. This means temperature conversion requires both multiplication and addition/subtraction (e.g., F = C × 9/5 + 32), unlike length or weight which are purely multiplicative.

What are SI base units?

The International System of Units (SI) defines 7 base units: meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance), and candela (luminous intensity). All other units are derived from these seven.

How do I derive a conversion formula?

Use dimensional analysis: write the known relationship between units, then set up a ratio. For example, since 1 inch = 2.54 cm, to convert inches to cm: multiply by 2.54/1. For chain conversions (e.g., miles to meters), multiply successive conversion factors: miles × 5280 ft/mile × 0.3048 m/ft.

Are these formulas exact or approximate?

Some conversions are defined exactly (1 inch = 2.54 cm exactly, 1 foot = 0.3048 m exactly). Others are measured values rounded for practical use (1 mile ≈ 1.60934 km). Temperature conversions between Celsius and Kelvin are exact (K = C + 273.15). We indicate precision in our worked examples.

Converters for these formulas

Use the published pair calculators that match the equations on this page.

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