Conversion Formula Encyclopedia
Every unit conversion is a multiplication or division by an exact conversion factor — or, in the case of temperature, a two-step linear transformation. This encyclopedia collects all the essential formulas in one place, organized by category, so you can look up the right formula and apply it immediately.
Each formula entry below includes the algebraic formula, a plain-English explanation of why the factor is what it is, a worked numeric example, and the most common use cases. For interactive conversions using these formulas on any value, use the linked converter tools in the sidebar.
How to Read These Formulas
Every conversion formula in this encyclopedia follows the pattern: [result unit] = [input unit] × [conversion factor]. The conversion factor is derived from the definition of the two units relative to each other. For example, because 1 inch is defined as exactly 2.54 centimeters, the factor from inches to centimeters is 2.54 (exact, no rounding). The inverse — centimeters to inches — is 1 ÷ 2.54 = 0.393701.
To use a formula: identify your input unit, locate the formula that converts from that unit to your target unit, substitute your value, and multiply. If you need to go in the other direction, either use the inverse formula (listed alongside) or divide by the factor instead of multiplying. A useful sanity check: converting forward and then backward should return the original number.
Length Conversion Formulas
━━━ INCHES ↔ CENTIMETERS ━━━ cm = in × 2.54 (exact, by international definition) in = cm × 0.393701 (= 1 ÷ 2.54) Example: 72 in × 2.54 = 182.88 cm (6 feet = 182.88 cm) ━━━ FEET ↔ METERS ━━━ m = ft × 0.3048 (exact: 1 ft = 12 in × 2.54 cm/in ÷ 100) ft = m × 3.28084 Example: 5 ft × 0.3048 = 1.524 m ━━━ MILES ↔ KILOMETERS ━━━ km = mi × 1.60934 mi = km × 0.62137 Example: 26.2 mi × 1.60934 = 42.165 km (marathon distance) ━━━ YARDS ↔ METERS ━━━ m = yd × 0.9144 (exact) yd = m × 1.09361 Example: 100 yd × 0.9144 = 91.44 m (US football field) ━━━ MILLIMETERS ↔ INCHES ━━━ mm = in × 25.4 (exact: 2.54 cm/in × 10 mm/cm) in = mm × 0.039370 Example: 12.7 mm × 0.039370 = 0.5 in (half-inch bolt)
Weight and Mass Conversion Formulas
━━━ POUNDS ↔ KILOGRAMS ━━━ kg = lb × 0.453592 lb = kg × 2.20462 Example: 185 lb × 0.453592 = 83.91 kg ━━━ OUNCES ↔ GRAMS ━━━ g = oz × 28.3495 oz = g × 0.035274 Example: 16 oz × 28.3495 = 453.59 g (= 1 lb) ━━━ POUNDS ↔ GRAMS ━━━ g = lb × 453.592 lb = g × 0.002205 Example: 0.5 lb × 453.592 = 226.80 g ━━━ KILOGRAMS ↔ GRAMS ━━━ g = kg × 1000 (exact) kg = g ÷ 1000 Example: 0.75 kg × 1000 = 750 g ━━━ STONE ↔ KILOGRAMS ━━━ kg = st × 6.35029 st = kg × 0.157473 Example: 11 st × 6.35029 = 69.85 kg (UK/Irish body weight)
Volume Conversion Formulas
━━━ GALLONS ↔ LITERS ━━━ L = gal × 3.78541 gal = L × 0.264172 Example: 10 gal × 3.78541 = 37.854 L ━━━ CUPS ↔ MILLILITERS ━━━ mL = cup × 236.588 cup = mL × 0.004227 Example: 2.5 cup × 236.588 = 591.47 mL ━━━ FLUID OUNCES ↔ MILLILITERS ━━━ mL = floz × 29.5735 floz = mL × 0.033814 Example: 8 fl oz × 29.5735 = 236.59 mL (= 1 US cup) ━━━ LITERS ↔ MILLILITERS ━━━ mL = L × 1000 (exact) L = mL ÷ 1000 Example: 0.33 L × 1000 = 330 mL (standard European beverage can) ━━━ TABLESPOONS ↔ TEASPOONS ━━━ tsp = tbsp × 3 (exact in US customary) tbsp = tsp ÷ 3 Example: 4 tbsp × 3 = 12 tsp (= ¼ cup)
Temperature Conversion Formulas
━━━ CELSIUS → FAHRENHEIT ━━━ °F = (°C × 9/5) + 32 °F = (°C × 1.8) + 32 Example: 100°C → (100 × 1.8) + 32 = 212°F (water boiling) ━━━ FAHRENHEIT → CELSIUS ━━━ °C = (°F − 32) × 5/9 °C = (°F − 32) ÷ 1.8 Example: 98.6°F → (98.6 − 32) ÷ 1.8 = 37°C (normal body temp) ━━━ CELSIUS → KELVIN ━━━ K = °C + 273.15 Example: 0°C + 273.15 = 273.15 K (freezing point of water) ━━━ KELVIN → CELSIUS ━━━ °C = K − 273.15 Example: 373.15 K − 273.15 = 100°C (boiling point at sea level) ━━━ FAHRENHEIT → KELVIN ━━━ K = (°F + 459.67) × 5/9 Example: 32°F → (32 + 459.67) × 5/9 = 273.15 K ━━━ QUICK MENTAL ESTIMATES ━━━ C→F: double °C and add 30 (accurate within ±2°F for 0–40°C) F→C: subtract 30 and halve (rough guide for everyday temps)
Area Conversion Formulas
━━━ SQUARE FEET ↔ SQUARE METERS ━━━ m² = ft² × 0.092903 ft² = m² × 10.7639 Example: 1,500 ft² × 0.092903 = 139.35 m² (typical US apartment) ━━━ ACRES ↔ HECTARES ━━━ ha = ac × 0.404686 ac = ha × 2.47105 Example: 5 ac × 0.404686 = 2.023 ha ━━━ SQUARE MILES ↔ SQUARE KILOMETERS ━━━ km² = mi² × 2.58999 mi² = km² × 0.386102 Example: 1 km² × 0.386102 = 0.386 mi² ━━━ ACRES ↔ SQUARE FEET ━━━ ft² = ac × 43,560 (exact) ac = ft² ÷ 43,560 Example: 2 ac × 43,560 = 87,120 ft² ━━━ SQUARE CENTIMETERS ↔ SQUARE INCHES ━━━ in² = cm² × 0.155000 cm² = in² × 6.45160 Example: 10 in² × 6.45160 = 64.52 cm²
Speed Conversion Formulas
━━━ MPH ↔ KM/H ━━━ km/h = mph × 1.60934 mph = km/h × 0.62137 Example: 65 mph × 1.60934 = 104.6 km/h (US highway speed) ━━━ KM/H ↔ METERS PER SECOND ━━━ m/s = km/h ÷ 3.6 km/h = m/s × 3.6 Example: 100 km/h ÷ 3.6 = 27.78 m/s ━━━ MPH ↔ METERS PER SECOND ━━━ m/s = mph × 0.44704 mph = m/s × 2.23694 Example: 60 mph × 0.44704 = 26.82 m/s ━━━ KNOTS ↔ MPH ━━━ mph = kn × 1.15078 kn = mph × 0.868976 Example: 250 kn × 1.15078 = 287.7 mph (typical cruising aircraft) ━━━ KNOTS ↔ KM/H ━━━ km/h = kn × 1.852 (exact) kn = km/h × 0.539957 Example: 500 km/h × 0.539957 = 270 kn
Time Conversion Formulas
━━━ SECONDS ↔ MINUTES ━━━ min = s ÷ 60 s = min × 60 Example: 90 s ÷ 60 = 1.5 min (1 min 30 sec) ━━━ MINUTES ↔ HOURS ━━━ hr = min ÷ 60 min = hr × 60 Example: 150 min ÷ 60 = 2.5 hr (2 hr 30 min) ━━━ HOURS ↔ DAYS ━━━ day = hr ÷ 24 hr = day × 24 Example: 48 hr ÷ 24 = 2 days ━━━ DAYS ↔ WEEKS ━━━ wk = day ÷ 7 day = wk × 7 Example: 21 day ÷ 7 = 3 weeks ━━━ SECONDS ↔ HOURS (DIRECT) ━━━ hr = s ÷ 3600 s = hr × 3600 Example: 7,200 s ÷ 3600 = 2 hr ━━━ DAYS ↔ SECONDS ━━━ s = day × 86,400 day = s ÷ 86,400 Example: 1 day × 86,400 = 86,400 s
Data Storage Conversion Formulas
━━━ DECIMAL (SI) SYSTEM — storage manufacturers, macOS ━━━
KB = B ÷ 1,000
MB = KB ÷ 1,000 = B ÷ 1,000,000
GB = MB ÷ 1,000 = B ÷ 1,000,000,000
TB = GB ÷ 1,000 = B ÷ 1,000,000,000,000
━━━ BINARY (IEC) SYSTEM — RAM, traditional Windows ━━━
KiB = B ÷ 1,024
MiB = KiB ÷ 1,024 = B ÷ 1,048,576
GiB = MiB ÷ 1,024 = B ÷ 1,073,741,824
TiB = GiB ÷ 1,024 = B ÷ 1,099,511,627,776
━━━ KEY CROSS-CONVERSIONS ━━━
MB to GB: GB = MB ÷ 1,000 Example: 500 MB = 0.5 GB
GB to TB: TB = GB ÷ 1,000 Example: 2,000 GB = 2 TB
GB to GiB: GiB = GB × 0.931323 Example: 1 GB = 0.931 GiB
Mbps to MB/s: MB/s = Mbps ÷ 8 Example: 100 Mbps = 12.5 MB/s
Key reason for discrepancy:
1 GiB = 1,073,741,824 B vs 1 GB = 1,000,000,000 B
Difference: 1 GiB is ~7.37% larger than 1 GBArea Conversion Formulas
━━━ SQUARE FEET ↔ SQUARE METERS ━━━ m² = ft² × 0.092903 ft² = m² × 10.7639 Example: 2,000 ft² × 0.092903 = 185.8 m² ━━━ ACRES ↔ HECTARES ━━━ ha = ac × 0.404686 ac = ha × 2.47105 Example: 25 ac × 0.404686 = 10.117 ha ━━━ SQUARE YARDS ↔ SQUARE METERS ━━━ m² = yd² × 0.836127 yd² = m² × 1.19599 Example: 100 yd² × 0.836127 = 83.6 m² ━━━ SQUARE MILES ↔ SQUARE KILOMETERS ━━━ km² = mi² × 2.58999 mi² = km² × 0.386102 1 mi² = 640 ac = 259.0 ha | 1 km² = 100 ha = 247.1 ac ━━━ IMPORTANT: AREA SCALES AS SQUARE OF LENGTH ━━━ 1 km = 1,000 m → 1 km² = 1,000² = 1,000,000 m² (not 1,000 m²) 1 ft = 0.3048 m → 1 ft² = 0.3048² = 0.092903 m²
Pressure Conversion Formulas
━━━ PSI ↔ KILOPASCAL (kPa) ━━━ kPa = PSI × 6.89476 PSI = kPa × 0.145038 Example: 35 PSI × 6.89476 = 241.3 kPa (typical car tire) ━━━ PSI ↔ BAR ━━━ bar = PSI × 0.068948 PSI = bar × 14.5038 Example: 2.5 bar × 14.5038 = 36.3 PSI ━━━ PSI ↔ ATMOSPHERE (atm) ━━━ atm = PSI × 0.068046 PSI = atm × 14.6959 1 atm = 14.696 PSI = 101.325 kPa = 1.01325 bar ━━━ PASCAL ↔ kPa ━━━ kPa = Pa ÷ 1,000 Pa = kPa × 1,000 Example: 101,325 Pa = 101.325 kPa = 1 atm ━━━ QUICK REFERENCE ━━━ Tire pressure: 30–35 PSI = 207–241 kPa = 2.07–2.41 bar 1 bar ≈ 1 atm ≈ 14.5 PSI (approximately, within 1.5%)
Energy Conversion Formulas
━━━ KILOWATT-HOURS ↔ BTU ━━━ BTU = kWh × 3,412.14 kWh = BTU × 0.000293071 Example: 5 kWh × 3,412.14 = 17,061 BTU ━━━ JOULES ↔ KILOWATT-HOURS ━━━ kWh = J ÷ 3,600,000 J = kWh × 3,600,000 Example: 1 kWh = 3,600,000 J (= 3.6 MJ) ━━━ JOULES ↔ CALORIES ━━━ cal = J ÷ 4.184 J = cal × 4.184 kcal = J ÷ 4,184 J = kcal × 4,184 Example: 200 kcal × 4,184 = 836,800 J (food Calories) ━━━ WATT-HOURS ↔ KILOWATT-HOURS ━━━ kWh = Wh ÷ 1,000 Wh = kWh × 1,000 Example: 75,000 Wh = 75 kWh (EV battery) ━━━ KEY RELATIONSHIPS ━━━ 1 kWh = 3,600 kJ = 3.6 MJ = 3,412 BTU = 860.4 kcal 1 BTU = 1,055 J = 0.000293 kWh = 0.252 kcal 1 kcal = 4,184 J = 4.184 kJ = 0.001163 kWh Note: food 'Calories' (capital C) = kcal
How to Apply Formulas Accurately
- ✓
Never round intermediate results. Carry full precision through the calculation and round only the final answer.
- ✓
Verify units cancel: write out 'km/hr × hr = km' to confirm the formula gives the unit you need.
- ✓
For temperature formulas, apply the operations in the correct order. For °F to °C: subtract 32 first, then multiply. Getting this backward gives a completely wrong answer.
- ✓
Use the exact factor when precision matters. For casual use, 0.45 is close enough for lbs to kg; for medical or engineering use, 0.453592 is required.
- ✓
When converting chains of units (e.g., miles → feet → inches), multiply all factors together first, then apply once — this reduces cumulative rounding error.
- ✓
Double-check direction with a known anchor. 1 kg ≈ 2.2 lb. If your formula gives 1 kg = 0.45 lb, you have divided when you should have multiplied.
- ✓
Area units require squaring the length conversion factor. 1 ft = 0.3048 m, so 1 ft² = 0.3048² = 0.092903 m² — not simply 0.3048 m².
- ✓
Pressure formulas use gauge vs. absolute: tire PSI is gauge (above atmosphere). Add 14.696 PSI to get absolute. Physics and chemistry equations require absolute pressure.
- ✓
Energy unit confusion: food 'Calories' (capital C) are kilocalories (kcal), not small calories (cal). 1 kcal = 1,000 cal = 4,184 J. HVAC BTU ratings are per hour (BTU/h), not total energy (BTU).
Frequently Asked Questions
What is the formula to convert miles to kilometers?
km = miles × 1.60934. This factor comes from the international definition: 1 mile = 5,280 feet, 1 foot = 0.3048 m, so 1 mile = 5,280 × 0.3048 = 1,609.344 meters = 1.609344 km. Example: 100 miles × 1.60934 = 160.934 km.
How do I convert kilograms to pounds?
lb = kg × 2.20462. The inverse direction is kg = lb × 0.453592. Example: 75 kg × 2.20462 = 165.35 lb. Quick estimate: multiply kg by 2.2.
What is the exact formula for Celsius to Fahrenheit?
°F = (°C × 9/5) + 32, equivalently °F = (°C × 1.8) + 32. Example: 37°C → (37 × 1.8) + 32 = 66.6 + 32 = 98.6°F (human body temperature). The formula has two steps: scale by 1.8 to account for the different degree sizes, then add 32 to account for the different zero points.
How do I convert liters to gallons?
US gallons = liters × 0.264172. Or: liters = US gallons × 3.78541. Example: 50 L × 0.264172 = 13.21 US gal. Note: UK imperial gallons are larger — 1 UK gallon = 4.54609 L (vs. 3.78541 L for US).
What formula converts square feet to square meters?
m² = ft² × 0.092903. The factor comes from (0.3048 m/ft)² = 0.092903 m²/ft². Example: 1,000 ft² × 0.092903 = 92.90 m². Reverse: ft² = m² × 10.7639.
How do I convert mph to km/h?
km/h = mph × 1.60934 (same factor as miles to kilometers, since both are distances per hour). Example: 60 mph × 1.60934 = 96.56 km/h. Reverse: mph = km/h × 0.62137.
What is the formula for converting gigabytes to terabytes?
TB = GB ÷ 1,000 (decimal, SI). Example: 2,500 GB ÷ 1,000 = 2.5 TB. In binary: TiB = GiB ÷ 1,024. Most everyday storage contexts use the decimal definition.
Why does temperature conversion need two steps but other conversions only need one?
Length, weight, and volume conversions all share the same zero point (0 inches = 0 cm; 0 kg = 0 lb). Temperature scales have different zero points: 0°C ≠ 0°F. This offset (32°F at the freezing point of water) requires addition/subtraction in addition to scaling. Kelvin has the same degree size as Celsius but a different zero (absolute zero), so °C ↔ K only requires addition of 273.15.
Is there a formula for knots to meters per second?
m/s = knots × 0.514444. This comes from: 1 knot = 1 nautical mile per hour = 1,852 m per 3,600 s = 0.51444 m/s. Example: 250 kn × 0.514444 = 128.61 m/s (a fast aircraft at cruise).
How do I convert tablespoons to milliliters?
mL = US tablespoons × 14.7868. Example: 4 tbsp × 14.7868 = 59.15 mL ≈ ¼ cup. For metric tablespoons (15 mL exactly, used in Australia, Canada): mL = tbsp × 15.
Related Tools
Length Converter
Apply length formulas with any input value.
Weight Converter
Apply weight formulas with any input value.
Temperature Converter
Apply temperature formulas instantly.
Volume Converter
Apply volume formulas with any input value.
Speed Converter
Convert between mph, km/h, knots, and m/s.
Area Converter
Apply area formulas for sq ft, acres, hectares.
Pressure Converter
Apply PSI, kPa, bar, and atm formulas.
Energy Converter
Apply kWh, BTU, joule, calorie formulas.
Related Converters
Related Guides
Complete Unit Conversion Handbook
25 min read
Conversion Formulas Handbook: Every Formula You Need
18 min read
Engineering Units Handbook: Pressure, Force, Energy, Power, and More
15 min read
International Measurement Guide: Metric, Imperial, and US Customary
12 min read
Measurement Systems Handbook: SI, Metric, Imperial, and US Customary
12 min read
Unit Conversion Dictionary: Common Units Defined and Cross-Referenced
15 min read
Sources
All conversion results are provided for general informational purposes only. Read our full disclaimer.