The metric system

The metric system is a system of measurement based on powers of 10. It measures length in meters, mass in grams and volume in liters, and adds prefixes such as kilo (1,000), centi (one hundredth) and milli (one thousandth) to make bigger and smaller units. Because every step is a power of 10, converting between metric units just means moving the decimal point. Its modern form is the International System of Units, or SI.

What is the metric system?

The metric system gives each kind of measurement one main unit, then builds every other unit from it by multiplying or dividing by 10. A kilometer is 1,000 meters, a centimeter is a hundredth of a meter, and a millimeter is a thousandth. Compare that with US customary units, where a foot is 12 inches, a yard is 3 feet and a mile is 5,280 feet.

In 1875, seventeen countries including the United States signed the Treaty of the Meter in Paris, which set up the international bodies that still look after the system. NIST represents the US in them. In the US, everyday measurements mostly use customary units, while science, medicine and many industries use metric.

Metric units

The scientific version, SI, has seven base units: the meter (length), kilogram (mass), second (time), ampere (electric current), kelvin (temperature), mole (amount of substance) and candela (brightness of light). Notice that the base unit of mass is the kilogram, not the gram. A liter is the volume of a cube 10 cm on each side, so 1 L = 1,000 cm³ and 1 mL = 1 cm³.

Metric prefixes

A prefix in front of a unit multiplies it by a power of 10. The same prefixes work with every unit: a kilometer is 1,000 meters, a kilogram is 1,000 grams and a kiloliter is 1,000 liters.

Prefixes are powers of 10, which links the metric system to scientific notation. Try writing a size as a power of 10 in this question from the Smallest Thing course.

How to convert metric units

Each step between neighboring prefixes in the kilo to milli list is a factor of 10. To convert:

• From a bigger unit to a smaller one, multiply: the number gets bigger. Move the decimal point right one place for each step.
• From a smaller unit to a bigger one, divide: the number gets smaller. Move the decimal point left one place for each step.

Example 1: kilometers to meters

3.5 km to meters: kilo to the base unit is 3 steps down, so multiply by 1,000. 3.5 × 1,000 = 3,500 m.

Example 2: milliliters to liters

250 mL to liters: milli to the base unit is 3 steps up, so divide by 1,000. 250 ÷ 1,000 = 0.25 L.

Example 3: millimeters to centimeters

78 mm to centimeters: one step up, so divide by 10. 78 ÷ 10 = 7.8 cm.

Example 4: kilograms to grams

4.2 kg to grams: multiply by 1,000 to get 4,200 g.

Metric to US customary conversions

Some conversion factors are exact by definition. Since 1959, the inch has been defined as exactly 2.54 cm and the pound as exactly 0.45359237 kg, so these values are exact, not rounded.

Example 5: inches to centimeters

A 12-inch ruler is 12 × 2.54 = 30.48 cm long.

Example 6: kilometers to miles

A 5 km race in miles: divide by 1.609344. 5 ÷ 1.609344 ≈ 3.11 miles.

Example 7: pounds to kilograms

150 lb in kilograms: 150 × 0.45359237 ≈ 68.04 kg.

Example 8: gallons to liters

2 US gallons: 2 × 3.785411784 ≈ 7.57 L.

Temperature: Celsius and Fahrenheit

Metric temperature is measured in degrees Celsius. Water freezes at 0°C (32°F) and boils at 100°C (212°F) at sea level. To convert:

A warm day of 25°C is 9/5 × 25 + 32 = 77°F. A body temperature of 98.6°F is 5/9 × (98.6 − 32) = 37°C. Scientists also use the kelvin, where 0 K is absolute zero and each kelvin is the same size as a degree Celsius.

Check your understanding.

Common mistakes

• Multiplying when you should divide. Smaller units mean a bigger number. If converting to a smaller unit gives a smaller number, something went wrong.
• Mixing up m and M. Lowercase m is milli (or meter), and uppercase M is mega. Symbols are case sensitive.
• Assuming every step is 10. Between kilo and the base unit there are three steps, so the factor is 1,000.
• Using an approximate factor where an exact one exists. 1 inch is exactly 2.54 cm.
• Squaring units incorrectly. 1 m = 100 cm, but 1 m² = 10,000 cm², because both sides of the square change.

Practice with a short timed paper

Unit conversions come up in math, science and everyday problem solving. The daily Pre-Algebra & Algebra 1 and Geometry, Algebra 2 & SAT Math papers are short timed practice tests of 8 questions, with a new one every day.

Read next

Physics · Practical skillsPhysics prefixes: list, powers of ten and conversionsEvery prefix you need for GCSE and A-level Physics, from tera to femto, with powers of ten, how to convert units, and worked examples from real physics.