How to Convert Units in Math and Science (Easy Guide)

Why Unit Conversion Matters

In math and science, getting the units right is just as important as getting the numbers right. A calculation with the wrong units is a wrong answer — even if the math is perfect.

Unit conversion is essential for:

• Science experiments — converting between lab measurements
• Physics problems — ensuring consistent units in formulas
• Everyday life — cooking recipes, travel, shopping internationally
• Standardized tests — many questions test conversion skills

Metric System Basics

The metric system is based on powers of 10, making conversions straightforward. Here are the key prefixes:

| Prefix | Symbol | Meaning | Example | |---|---|---|---| | kilo- | k | × 1000 | 1 km = 1000 m | | hecto- | h | × 100 | 1 hm = 100 m | | deca- | da | × 10 | 1 dam = 10 m | | (base) | — | × 1 | 1 m, 1 g, 1 L | | deci- | d | × 0.1 | 1 dm = 0.1 m | | centi- | c | × 0.01 | 1 cm = 0.01 m | | milli- | m | × 0.001 | 1 mm = 0.001 m |

The staircase method: Moving to a smaller unit? Multiply (move the decimal right). Moving to a larger unit? Divide (move the decimal left).

The Factor-Label Method

The factor-label method (also called dimensional analysis) is the most reliable way to convert units. It works for any conversion.

How it works:

1. Write the value you want to convert
2. Multiply by a conversion factor (a fraction equal to 1)
3. Make sure the unwanted units cancel out
4. Calculate

Example: Convert 5 km to meters

5 km × (1000 m / 1 km) = 5000 m

The "km" cancels, leaving meters.

Example: Convert 250 mL to liters

250 mL × (1 L / 1000 mL) = 0.25 L

The "mL" cancels, leaving liters.

Common Metric Conversions

Length

• 1 km = 1000 m
• 1 m = 100 cm
• 1 m = 1000 mm
• 1 cm = 10 mm

Mass

• 1 kg = 1000 g
• 1 g = 1000 mg
• 1 metric ton = 1000 kg

Volume

• 1 L = 1000 mL
• 1 mL = 1 cm³
• 1 m³ = 1000 L

Quick examples:

• 3.5 kg = 3500 g (multiply by 1000)
• 450 cm = 4.5 m (divide by 100)
• 2.8 L = 2800 mL (multiply by 1000)

Metric to Imperial Conversions

These conversions aren't as clean as metric-to-metric, but they come up often:

Length

• 1 inch = 2.54 cm
• 1 foot = 30.48 cm
• 1 mile = 1.609 km
• 1 meter ≈ 3.281 feet

Mass

• 1 pound (lb) ≈ 0.4536 kg
• 1 kg ≈ 2.205 lbs
• 1 ounce (oz) ≈ 28.35 g

Volume

• 1 gallon ≈ 3.785 L
• 1 liter ≈ 0.264 gallons
• 1 cup ≈ 236.6 mL

Example: Convert 10 miles to kilometers

10 miles × 1.609 km/mile = 16.09 km

Example: Convert 150 lbs to kg

150 lbs × 0.4536 kg/lb = 68.04 kg

Temperature Conversions

Temperature uses different formulas depending on the scales:

Celsius to Fahrenheit

°F = (°C × 9/5) + 32

Example: 25°C = (25 × 9/5) + 32 = 45 + 32 = 77°F

Fahrenheit to Celsius

°C = (°F − 32) × 5/9

Example: 98.6°F = (98.6 − 32) × 5/9 = 66.6 × 5/9 = 37°C

Celsius to Kelvin

K = °C + 273.15

Example: 0°C = 0 + 273.15 = 273.15 K

Key reference points:

| | °C | °F | K | |---|---|---|---| | Water freezes | 0 | 32 | 273.15 | | Water boils | 100 | 212 | 373.15 | | Room temp | ~20 | ~68 | ~293 | | Body temp | 37 | 98.6 | 310.15 |

Multi-Step Conversions

Sometimes you need to chain multiple conversion factors:

Example: Convert 5 km/h to m/s

5 km/h × (1000 m / 1 km) × (1 h / 3600 s) = 5000 / 3600 m/s = 1.39 m/s

Example: Convert 3 cubic feet to liters

3 ft³ × (30.48 cm / 1 ft)³ × (1 mL / 1 cm³) × (1 L / 1000 mL) = 3 × 28316.85 cm³ / 1000 = 84.95 L

For more on speed conversions, see our speed, distance, and time guide.

Practice Problems

1. Convert 8500 g to kg
2. Convert 3.2 miles to km
3. Convert 72°F to °C
4. Convert 500 mm to m
5. Convert 90 km/h to m/s

Answers: (1) 8.5 kg (2) 5.15 km (3) 22.2°C (4) 0.5 m (5) 25 m/s

Need More Help?

Unit conversions come up constantly in math, physics, and chemistry. Mr Jarven AI Tutor can convert any unit, explain the method, and give you practice problems.

👉 Ask Mr Jarven AI Tutor for instant unit conversion help.