Learn the metric units for length, mass and capacity, how prefixes work, how to convert in both directions, how area and volume factors differ, how to compare prices, and how accurate a measurement can be.
Every time you buy rice, fill a bottle, measure a room or read a medicine label you use measurement. The metric system is built so that these quantities connect through powers of ten, and once you understand why, conversions become a short reasoning step instead of a trick with the decimal point. This guide covers length, mass and capacity, the prefixes behind the units, converting in both directions, adding and comparing measurements, and the links between length, area, volume and capacity. It also covers how to read scales correctly, how accurate a measurement can be, and the history of the units, including the parts that are defined differently today.
Measuring means comparing a quantity with an agreed standard unit. Saying a table is 2 metres long means it is two times the length of the standard metre. Three quantities appear most often at school level:
| Quantity | It tells us | Common metric units |
|---|---|---|
| Length | How long, tall, wide or far | km, m, cm, mm |
| Mass | How much matter an object contains | t, kg, g, mg |
| Capacity | How much a container can hold | kL, L, mL |
The unit must always be written. A distance of 5 km is very different from 5 m, and 5 g is very different from 5 kg.
Mass and weight. In science, mass is the amount of matter in an object (measured in kg), while weight is the pull of gravity on it, which is a force measured in newtons. In everyday speech and in many exam questions, “weighs 2.4 kg” is used to mean “has a mass of 2.4 kg”. This article uses mass.
A prefix tells you how a unit relates to the base unit. The same prefixes work for metres, grams and litres.
| Prefix | Symbol | Factor | Example |
|---|---|---|---|
| giga | G | 1 000 000 000 | 1 GB of data (a billion bytes) |
| mega | M | 1 000 000 | 1 megametre = 1 000 000 m |
| kilo | k | 1000 | 1 km = 1000 m |
| hecto | h | 100 | 1 hectare = 100 ares |
| deca | da | 10 | 1 dam = 10 m |
| (base unit) | 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 |
| micro | µ | 0.000 001 | 1 µm = 0.000 001 m |
| nano | n | 0.000 000 001 | 1 nm = one billionth of a metre |
The symbol m can mean “metre” or “milli”, so the position matters: in “mm” the first m is milli and the second is metre. A tonne (t) is a metric unit equal to 1000 kg.
Careful: in the SI system the base unit of mass is the kilogram, not the gram, even though we usually think of the gram as the basic unit. The litre is not an SI base unit either (the SI unit of volume is the cubic metre), but it is accepted for everyday use alongside SI.
| Relationship | Meaning |
|---|---|
| 1 km = 1000 m | one thousand metres in a kilometre |
| 1 m = 100 cm | one hundred centimetres in a metre |
| 1 cm = 10 mm | ten millimetres in a centimetre |
| 1 m = 1000 mm | 100 × 10 = 1000 |
You need more small units to make the same length, so the number gets bigger.
(a) 4.7 m to cm: 4.7 × 100 = 470 cm. (b) 6.25 km to m: 6.25 × 1000 = 6250 m. (c) 2.4 km to cm: 2.4 × 1000 = 2400 m, then 2400 × 100 = 240 000 cm (km to m, then m to cm).
(a) 375 cm to m: 375 ÷ 100 = 3.75 m. (b) 2450 mm to m: 2450 ÷ 1000 = 2.45 m. (c) 2500 m to km: 2500 ÷ 1000 = 2.5 km.
Is a metre bigger or smaller than a centimetre?
The fix: there are 100 cm in 1 m, so divide by 100, not 10: 250 ÷ 100 = 2.5 m. Do a size check as well: a metre is a bigger unit, so the number must get smaller, and 25 is far too large for a 250 cm object (about a tall door). Check the factor, then check the direction.
| Relationship | Meaning |
|---|---|
| 1 t = 1000 kg | a tonne |
| 1 kg = 1000 g | one thousand grams |
| 1 g = 1000 mg | one thousand milligrams |
| 1 kg = 1 000 000 mg | 1000 × 1000 |
(a) 3.6 kg to g: 3.6 × 1000 = 3600 g. (b) 2500 g to kg: 2500 ÷ 1000 = 2.5 kg. (c) 4.2 g to mg: 4.2 × 1000 = 4200 mg. (d) 850 mg to g: 850 ÷ 1000 = 0.85 g.
(e) 0.045 kg to mg. Milligrams are far smaller than kilograms, so the number must grow a lot. 1 kg = 1 000 000 mg, so 0.045 × 1 000 000 = 45 000 mg. (Check: 0.045 kg = 45 g, and 45 × 1000 = 45 000 mg.)
How many grams are in a whole kilogram?
The fix: kg to g means × 1000, so 0.8 × 1000 = 800 g. Moving the decimal point by three places needs a place holder zero: 0.8 becomes 800, not 80. A quick check: 0.8 kg is nearly a kilogram, so about 800 g is sensible and 80 g is not.
Capacity is how much a container can hold. A litre is a convenient unit for liquids, and 1 L = 1000 mL. A kilolitre is 1000 L.
(a) 1.75 L to mL: 1.75 × 1000 = 1750 mL. (b) 650 mL to L: 650 ÷ 1000 = 0.65 L. (c) 0.375 L = 375 mL. (d) A recipe needs 1.25 L, and the jug is marked in mL: 1.25 × 1000 = 1250 mL.
Since 1964 the litre has been defined as exactly one cubic decimetre, which is a cube with edges of 10 cm. Its volume is 10 × 10 × 10 = 1000 cm³. So 1 L = 1000 cm³ and 1 mL = 1 cm³.
Water has a convenient property: 1 mL of water has a mass of about 1 g, so 1 L of water has a mass of about 1 kg (this is true for pure water and is a close approximation at ordinary temperatures). The metric system was designed this way.
Be careful with squared and cubed units. When both lengths change units, the conversion factor is squared.
| Conversion | Why |
|---|---|
| 1 m² = 10 000 cm² | 100 × 100 |
| 1 cm² = 100 mm² | 10 × 10 |
| 1 km² = 1 000 000 m² | 1000 × 1000 |
| 1 hectare = 10 000 m² | a square 100 m by 100 m |
| 1 m³ = 1 000 000 cm³ | 100 × 100 × 100 |
| 1 m³ = 1000 L | 1 000 000 cm³ ÷ 1000 cm³ per litre |
The word hectare comes from “hecto-are”: an are is 100 m² and a hectare is 100 ares.
(a) 5.2 m² to cm²: 5.2 × 10 000 = 52 000 cm². (b) 3.5 m³ to litres: 3.5 × 1000 = 3500 L.
(c) A rectangular plot is 20 m by 15 m. Area = 300 m² = 300 ÷ 10 000 = 0.03 hectare.
(d) A tank 2 m long, 1.5 m wide and 1 m deep holds 2 × 1.5 × 1 = 3 m³ = 3000 L. Filled with water, it has a mass of about 3000 kg = 3 tonnes.
How many 1 cm by 1 cm squares fit in a 1 m by 1 m square?
The fix: an area has two lengths. A square metre is 100 cm by 100 cm, so it contains 100 × 100 = 10 000 small squares. For cubic units the factor is cubed: 1 m³ = 100 × 100 × 100 = 1 000 000 cm³. Square the length factor for area and cube it for volume.
You can only add, subtract or compare measurements in the same unit. Convert first.
(a) A ribbon of 2 m and another of 75 cm: 75 cm = 0.75 m, so 2 + 0.75 = 2.75 m. A common error is to write 2 + 75 = 77.
(b) 1.8 kg of flour plus 650 g: 650 g = 0.65 kg, so 1.8 + 0.65 = 2.45 kg.
(c) Bottle A holds 750 mL and bottle B holds 1.2 L = 1200 mL. Difference = 1200 − 750 = 450 mL.
(d) Repeated amounts. A café uses 250 mL of milk per drink. For 18 drinks: 18 × 250 = 4500 mL = 4.5 L. A factory packs 24 bags of 350 g: 24 × 350 = 8400 g = 8.4 kg.
(e) Leftover. A jug holds 1.2 L. Seven glasses of 150 mL are poured. Used: 7 × 150 = 1050 mL, and 1.2 L = 1200 mL, so 150 mL is left.
(f) Medicine. A dose of 5 mL, three times a day for 7 days: 5 × 3 × 7 = 105 mL.
(g) Comparing size. A shelf is 1.8 m = 1800 mm long and a gap is 12 mm, so the shelf is 1800 ÷ 12 = 150 times the gap.
What is missing from the answer?
The fix: the answer has no unit, and the numbers were added as though both were in the same unit. 2 m is 200 cm, so 200 + 75 = 275 cm = 2.75 m. Always convert both to one unit first and then write the unit with the answer.
To compare prices, convert to the same unit and find the price per unit. One pack has 750 g for Rs 270, and another has 1.2 kg for Rs 408. Price per kg: 270 ÷ 0.75 = Rs 360 for the first pack, and 408 ÷ 1.2 = Rs 340 for the second. The larger pack is cheaper per kilogram.
| What you measure | Sensible unit |
|---|---|
| Distance between towns | km |
| Length of a room | m |
| Length of a pencil | cm |
| Thickness of a coin or paper | mm |
| Mass of a person, a bag of rice | kg |
| Mass of a spice or a letter | g |
| A dose of medicine, a drink | mL |
| A fuel tank, a bucket | L |
| A truck load, a ship | tonnes |
Estimating gives a useful check. A rough guide: a door is about 2 m high, a pencil about 18 cm, a mobile phone about 150 g, a cup about 250 mL, a bottle of drinking water 500 mL to 1.5 L, a bag of flour 1 kg. If an answer says a pencil is 18 m long, the unit or the factor is wrong.
Start from the zero mark, read the whole centimetres, then count the small marks for millimetres. Look straight at the mark, not from the side, to avoid a reading error caused by the angle.
Every measurement is rounded to the precision of the instrument. A length given as 12 cm to the nearest centimetre could be any value from 11.5 cm up to (but not including) 12.5 cm: 11.5 ≤ length < 12.5. A mass of 4.2 kg to one decimal place lies in 4.15 ≤ mass < 4.25. In general the error can be up to half of the smallest unit used.
6 feet = 6 × 30.48 = 182.88 cm. 5 miles ≈ 5 × 1.609 = 8.05 km. 2.5 pounds ≈ 2.5 × 0.4536 = 1.13 kg.
The metric system was developed in France in the 1790s. The metre was first defined as one ten-millionth of the distance from the North Pole to the equator along the meridian through Paris, and surveyors measured part of that distance to fix its length. The gram was first based on the mass of a cubic centimetre of water, and the kilogram became the base unit. Over the years the definitions were improved. Since 1983 the metre has been defined using the speed of light (the distance light travels in 1/299 792 458 of a second), and since 2019 the kilogram has been defined using a fixed value of a constant of nature, the Planck constant, instead of a metal cylinder kept in France. These changes did not alter the everyday size of the units, but they made them reproducible anywhere.
A cube of water 10 cm on each side holds 1 litre and has a mass of about 1 kilogram. The units for length, capacity and mass are connected by design: this is the main reason the metric system is so easy to use.
Choose a kind of measurement, type a value, and pick the units. The converter gives the answer, the conversion factor, and a size check so you can see whether the number should grow or shrink.
Add or subtract two measurements that are given in different units. The calculator changes both to the unit you choose for the answer and shows the converted values, just as you should in your working.
Tap the correct answer for each question. Your best score is saved on this device.
1. 0.6 km = 0.6 × 1000 = 600 m, and 600 × 100 = 60 000 cm. 7250 mL = 7250 ÷ 1000 = 7.25 L.
2. 2.5 kg = 2500 g, and 2500 ÷ 250 = 10 packets.
3. 3.2 × 10 000 = 32 000 cm².
1. (a) 0.045 × 1 000 000 = 45 000 mg. (b) 3.6 × 1000 = 3600 m, then × 100 = 360 000 cm. (c) 2750 ÷ 1000 = 2.75 L.
2. 2 m 75 cm = 2.75 m. 1 m 40 cm = 1.40 m. Total = 2.75 + 1.40 = 4.15 m (that is, 4 m 15 cm).
3. Used = 7 × 150 = 1050 mL. 1.2 L = 1200 mL. Left = 1200 − 1050 = 150 mL.
4. Volume = 2 × 1.5 × 1 = 3 m³. 1 m³ = 1000 L, so the tank holds 3000 L. Water has a mass of about 1 kg per litre, so the mass is about 3000 kg = 3 tonnes.
5. 750 g = 0.75 kg, so the first pack costs 270 ÷ 0.75 = Rs 360 per kg. The second costs 408 ÷ 1.2 = Rs 340 per kg. The 1.2 kg pack is better value.
6. Lower bound 11.5 cm; upper bound 12.5 cm (the true length satisfies 11.5 ≤ length < 12.5).
7. Area = 20 × 15 = 300 m² = 300 ÷ 10 000 = 0.03 hectare. Fuel: 350 ÷ 100 = 3.5, and 3.5 × 8 = 28 litres.
Measurement is best learned with real objects. Ask learners to estimate first and then measure: the width of a desk, the mass of a bag, the capacity of a cup. Fill a litre bottle with water and use a 10 cm cube or a balance to show that 1 L is 1000 cm³ and about 1 kg. The most common errors are the direction of conversion and using the wrong factor for area, so insist on a size check every time. Use unit prices when shopping or cooking to make the topic real. The Unit Converter and Measurement Calculator on this page show the factor and direction for every conversion, so learners can compare their own working.
For further reading, the International Bureau of Weights and Measures (BIPM) publishes the official SI system and its definitions of the units. This article is original EDUSAMBAM writing. Examination requirements differ between boards, so compare your practice with the specification of your own board.
20 questions covering metric units, conversion direction, metres, litres, grams, decimals and real-life measurement. Answer every question, then submit to see your score instantly.