Convert between metric and imperial units instantly with step-by-step explanations. Length, weight, temperature, volume, energy, pressure, and more — perfect for high school, AP, and SAT revision.
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Unit conversion is the process of expressing a measurement in different units without changing its actual value. For example, 1 kilometer and 1000 meters are the same distance — just expressed in different units.
The key to unit conversion is the conversion factor— a ratio that equals 1. Since multiplying by 1 doesn't change a value, multiplying by a conversion factor changes the units but not the quantity.
The Conversion Factor Method
value (new unit) = value (old unit) × conversion factor
Example: 5 miles × 1.609 km/mile = 8.045 km
Dimensional analysis is a systematic method for converting units by treating them as algebraic quantities that can be cancelled. This technique is essential in high school and AP science.
Example: Convert 72 km/h to m/s
72 km/h × (1000 m / 1 km) × (1 h / 3600 s)
= 72 × 1000 / 3600 m/s
= 20 m/s
Notice how the km and h units cancel, leaving just m/s. This works for any chain of conversions.
The International System of Units (SI) is used by 95% of the world's population. Its base-10 structure makes calculations straightforward.
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| Tera | T | 10¹² = 1,000,000,000,000 | 1 TB = 10¹² bytes |
| Giga | G | 10⁹ = 1,000,000,000 | 1 GHz = 10⁹ Hz |
| Mega | M | 10⁶ = 1,000,000 | 1 MW = 10⁶ W |
| Kilo | k | 10³ = 1,000 | 1 km = 1,000 m |
| Hecto | h | 10² = 100 | 1 hPa = 100 Pa |
| Deca | da | 10¹ = 10 | 1 dag = 10 g |
| (base) | — | 10⁰ = 1 | meter, gram, liter |
| Deci | d | 10⁻¹ = 0.1 | 1 dL = 0.1 L |
| Centi | c | 10⁻² = 0.01 | 1 cm = 0.01 m |
| Milli | m | 10⁻³ = 0.001 | 1 mm = 0.001 m |
| Micro | μ | 10⁻⁶ = 0.000001 | 1 μm = 10⁻⁶ m |
| Nano | n | 10⁻⁹ | 1 nm = 10⁻⁹ m |
| Pico | p | 10⁻¹² | 1 pF = 10⁻¹² F |
Key insight: To convert between metric prefixes, just count the steps on the staircase and move the decimal point that many places.
Example: 3.5 km → m = move decimal 3 places right = 3,500 m
Used in: Most countries worldwide, all scientific research, international trade
Used in: United States, Myanmar, Liberia; UK uses for road signs, pints, and body measurements
1 km = 1,000 m
1 m = 100 cm
1 cm = 10 mm
1 mile = 1.609 km
1 mile = 5,280 ft
1 yard = 3 ft
1 foot = 12 inches
1 inch = 2.54 cm
1 nautical mile = 1.852 km
1 m = 3.281 ft
1 kg = 1,000 g
1 g = 1,000 mg
1 metric ton = 1,000 kg
1 lb = 16 oz
1 stone = 14 lbs
1 US ton = 2,000 lbs
1 kg = 2.205 lbs
1 lb = 0.4536 kg
1 oz = 28.35 g
1 stone = 6.350 kg
| Event | °C | °F | K |
|---|---|---|---|
| Absolute zero | -273.15 | -459.67 | 0 |
| Water freezes | 0 | 32 | 273.15 |
| Room temperature | 20-22 | 68-72 | 293-295 |
| Body temperature | 37 | 98.6 | 310.15 |
| Water boils | 100 | 212 | 373.15 |
1 L = 1,000 mL
1 m³ = 1,000 L
1 mL = 1 cm³
1 US gallon = 3.785 L
1 UK gallon = 4.546 L
1 US pint = 473 mL
1 UK pint = 568 mL
1 cup = 237 mL
1 fl oz = 29.6 mL
1 tablespoon = 15 mL
Note: US and UK pints and gallons are different sizes. Always specify which system!
Avoid these frequent errors that cost students marks in high school and AP exams.
✗ Wrong
5 km to miles: 5 × 1.609 = 8.045 miles
✓ Correct
5 km to miles: 5 ÷ 1.609 = 3.107 miles
Miles are bigger than km, so you need fewer of them. Always check: is the target unit bigger or smaller?
✗ Wrong
10 gallons = 37.85 L (assuming US) when the question means UK
✓ Correct
10 UK gallons = 45.46 L | 10 US gallons = 37.85 L
A UK gallon is about 20% larger than a US gallon. In the UK, pints of milk and beer are 568 mL, not 473 mL.
✗ Wrong
0°C × 1.8 = 0°F
✓ Correct
0°C × 1.8 + 32 = 32°F
Temperature conversion requires both multiplication AND addition. Water freezes at 0°C but 32°F — the scales have different zero points.
✗ Wrong
Converting 10 kg directly to Newtons by dividing
✓ Correct
Weight = mass × g → 10 kg × 9.81 = 98.1 N
Kilograms measure mass. Newtons measure force (weight). Use W = mg to convert between them.
✗ Wrong
1 km = 100 m (thinking kilo = hundred)
✓ Correct
1 km = 1,000 m (kilo = thousand)
kilo = 1000, hecto = 100, deca = 10. Getting this wrong makes your answer off by a factor of 10.
✗ Wrong
Converting miles directly to centimeters in one step
✓ Correct
miles → meters → centimeters (two simple steps)
Going via the base unit (meters for length, grams for mass) makes each step straightforward and easy to verify.
Step-by-step solutions to common exam questions.
Step 1: Recall that 1 mile = 1.609 km
Step 2: Multiply: 5.2 × 1.609 = 8.3668
Step 3: Round to 3 significant figures: 8.37 km
Check: 5.2 miles should be more than 5.2 km (since km are smaller). 8.37 > 5.2 ✓
Step 1: Write the formula: °C = (°F - 32) × 5/9
Step 2: Substitute: °C = (98.6 - 32) × 5/9
Step 3: Calculate: °C = 66.6 × 5/9 = 66.6 × 0.5556 = 37°C
This is normal body temperature — a useful benchmark to memorise.
Step 1: Convert meters to kilometers: divide by 1000
Step 2: Convert seconds to hours: multiply by 3600 (60 × 60)
Step 3: Combined: 340 × 3600 / 1000 = 340 × 3.6 = 1224 km/h
Shortcut: to convert m/s to km/h, just multiply by 3.6. This is the speed of sound at sea level!
Step 1: Recall: 1 kWh = 1 kW × 1 hour = 1000 W × 3600 s
Step 2: Since 1 W = 1 J/s: 1 kWh = 1000 × 3600 J = 3,600,000 J
Step 3: Therefore: 2.5 kWh = 2.5 × 3,600,000 = 9,000,000 J = 9 MJ
This is a common AP physics conversion. Remember: kWh is an energy unit (power × time), not a power unit.
1 mile = 1.609344 kilometers (exactly). To convert miles to km, multiply by 1.609. To convert km to miles, divide by 1.609.
Use the formula: °C = (°F - 32) × 5/9. Subtract 32 first, then multiply by 5/9. Example: 100°F = (100-32) × 5/9 = 37.78°C.
1 kilogram = 2.205 pounds. To convert kg to lbs, multiply by 2.205. To convert lbs to kg, multiply by 0.4536.
US gallon = 3.785 liters. UK (imperial) gallon = 4.546 liters. The UK gallon is about 20% larger. This also affects pints, quarts, and fluid ounces.
1 meter = 3.281 feet. 1 foot = 0.3048 meters (exactly). This is one of the internationally agreed exact conversion factors.
Absolute zero = 0 K = −273.15°C = −459.67°F. It is the theoretical lowest temperature, where all thermal motion ceases.
Metric uses base-10 units (meters, kilograms, liters) used by 95% of the world. Imperial uses feet, pounds, gallons, primarily in the US. Metric is easier for calculations.
Metric prefixes are powers of 10: kilo (k) = 1000, centi (c) = 0.01, milli (m) = 0.001. To convert, move the decimal point the appropriate number of places.
Square the linear conversion factor. Since 1 m = 100 cm, then 1 m² = 10,000 cm² (100²). Similarly, 1 km² = 1,000,000 m².
Yes! This tool covers all unit conversions required for high school, AP, and SAT Math, Physics, and Chemistry. Learn Mode helps you practice the method for exam conditions.
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