Every measurement compares a quantity to a standard unit. Learn the ladder of metric units and the exact pattern for converting length, mass, capacity, time, area and speed.
A tailor cuts cloth in metres and centimetres. A pharmacist weighs in grams and milligrams. A farmer buys water by the litre and measures land by the hectare. All of them depend on one idea: a measurement is only useful when everyone uses the same units, and when you can change from one unit to another without making a mistake. This article gives you the exact pattern for doing that for length, mass, capacity, time, area and volume.
Measurement means comparing a quantity to an agreed, standard unit. Saying “the table is 2 metres long” only means something because everyone agrees on exactly how long a metre is. Long ago, people measured with body parts such as the hand, the foot and the cubit (the length of the forearm). The problem was obvious: your foot is not the same size as mine. Standard units solved that problem, so that a shopkeeper in Karachi and an engineer in Lahore mean the same thing by “one kilogram”.
Every measurement has two parts: a number and a unit. “5” alone means nothing, but “5 cm” and “5 km” are very different. Always write the unit.
Most of the world uses the metric system, which is built entirely around powers of 10. Every unit shares the same small set of prefixes, so learning them once unlocks length, mass and capacity at the same time.
| Prefix | Meaning | Multiplier |
|---|---|---|
| kilo- | one thousand | ×1,000 |
| (base unit) | metre, gram, litre | ×1 |
| centi- | one hundredth | ×0.01 |
| milli- | one thousandth | ×0.001 |
So a kilometre is 1,000 metres, a millilitre is one thousandth of a litre, and a centimetre is one hundredth of a metre. (Centi- means “hundred”, like the word century, and milli- means “thousand”, like the word millennium.) For a complete list of official prefixes, including very large and very small ones, see the link in Further Reading.
| Unit | Symbol | Equal To |
|---|---|---|
| Millimetre | mm | 0.1 cm |
| Centimetre | cm | 10 mm |
| Metre | m | 100 cm = 1,000 mm |
| Kilometre | km | 1,000 m |
It helps to know a few real sizes so you can judge whether an answer is sensible. A fingernail is about 1 cm wide. A door is about 2 m high. A cricket pitch is 22 yards long, which is about 20.12 m. A steady walk covers about 1 km in 10 to 15 minutes.
| Unit | Symbol | Equal To |
|---|---|---|
| Milligram | mg | 0.001 g |
| Gram | g | 1,000 mg |
| Kilogram | kg | 1,000 g |
| Tonne | t | 1,000 kg |
In everyday talk we say “weight”, but in science mass is the amount of matter in an object, and it is measured in grams and kilograms. A bag of sugar is about 1 kg. A mango is roughly 300 g. A large truck load might be measured in tonnes. A tonne here means the metric tonne of 1,000 kg.
| Unit | Symbol | Equal To |
|---|---|---|
| Millilitre | mL | 0.001 L |
| Litre | L | 1,000 mL |
| Kilolitre | kL | 1,000 L |
A teaspoon holds about 5 mL, a glass of water about 250 mL, and a large bottle of drink 1.5 L. Capacity also links to volume: 1 mL = 1 cm³, so 1 L = 1,000 cm³, and 1 m³ = 1,000 L. One litre of water has a mass of about 1 kg, which is why cooks and scientists often treat millilitres and grams of water as equal.
Picture every metric unit sitting on rungs of a ladder, biggest at the top. Moving down the ladder (bigger unit to smaller unit) means multiplying. Moving up the ladder (smaller unit to bigger unit) means dividing. The number you multiply or divide by is always the conversion factor between those two rungs.
Smaller unit values mean you need more of them to describe the same amount (many small mm), while bigger unit values mean you need fewer of them (few large km). More of a smaller unit, fewer of a bigger unit: multiply going smaller, divide going bigger.
Convert 3,500 m to km. Since 1 km = 1,000 m, divide by 1,000: 3,500 ÷ 1,000 = 3.5 km.
Convert 4,200 g to kg. Divide by 1,000: 4,200 ÷ 1,000 = 4.2 kg. And 350 mg to g: divide by 1,000 to get 0.35 g.
Convert 3,600 mL to L. Divide by 1,000: 3,600 ÷ 1,000 = 3.6 L.
Convert 2.5 km to m. Multiply by 1,000: 2.5 × 1,000 = 2,500 m.
Convert 0.8 tonne to kg. Multiply by 1,000: 0.8 × 1,000 = 800 kg.
Convert 2.75 L to mL. Multiply by 1,000: 2.75 × 1,000 = 2,750 mL.
It is easy to forget which direction the operation goes once several units are involved.
The fix: going from a smaller unit to a bigger one always means dividing, because it takes many small units to make one big one. 4,500 mm to m: divide by 1,000 (since 1 m = 1,000 mm), giving 4.5 m, not 4,500,000 m.
Before you finish, ask: “Should my number get bigger or smaller?” If you change to a smaller unit (km to m), you need more of them, so the number must grow. If you change to a bigger unit (g to kg), the number must shrink. If your answer goes the wrong way, you used the wrong operation.
(a) Write 3 m 45 cm in centimetres: 3 m = 300 cm, so 300 + 45 = 345 cm.
(b) Write 2 kg 350 g in kilograms: 2 kg 350 g = 2,350 g ÷ 1,000 = 2.35 kg.
(c) Work out 5 m − 2 m 35 cm. Change everything to centimetres: 500 − 235 = 265 cm = 2 m 65 cm, or 2.65 m.
Never add or subtract numbers with different units. “2 m + 35 cm” is not 37 of anything.
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Time is the one measurement that does not follow the metric system’s powers of 10. Its conversion factors come from history and astronomy instead (the 60 comes from an ancient counting system).
| Unit | Equal To |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes = 3,600 seconds |
| 1 day | 24 hours |
| 1 week | 7 days |
150 seconds = 2 minutes and 30 seconds (150 ÷ 60 = 2 remainder 30). 2.5 hours = 2.5 × 60 = 150 minutes. 3 days = 3 × 24 = 72 hours.
Because the decimal point looks like “20”, many students read 0.2 hours as 20 minutes.
The fix: time is not in tens. Convert the decimal part by multiplying by 60. 0.2 hours = 0.2 × 60 = 12 minutes, so 1.2 hours = 1 hour 12 minutes. In the other direction, 3 h 45 min = 3 + 45/60 = 3.75 hours.
For clocks, the 12-hour and 24-hour systems and timetables, see the time page linked at the end of this article.
Area units look similar to length units, but converting between them is not the same simple ×10 or ÷10 pattern. Area is length squared, so the conversion factor gets squared too.
Since 1 m = 100 cm, squaring both sides gives 1 m² = 100 cm × 100 cm = 10,000 cm², not 100 cm² as the length conversion might suggest.
Applying the length conversion factor directly to an area is one of the most common measurement mistakes.
The fix: since 1 m² = 10,000 cm², divide by 10,000, not 100. 50,000 cm² ÷ 10,000 = 5 m². Any time a unit is squared (like cm² or m²), its conversion factor must be squared too.
| Unit | Equal To |
|---|---|
| 1 m² | 10,000 cm² |
| 1 hectare | 10,000 m² (a 100 m × 100 m square) |
| 1 km² | 1,000,000 m² |
The same idea works for volume, but with the factor cubed: 1 m³ = 100 × 100 × 100 = 1,000,000 cm³. Combined with 1 L = 1,000 cm³, this means 1 m³ = 1,000 L.
(a) Convert 3.5 m² to cm²: multiply by 10,000, giving 35,000 cm².
(b) A farm covers 2.5 hectares. In square metres that is 2.5 × 10,000 = 25,000 m².
(c) A water tank is 2 m long, 1.5 m wide and 0.8 m high. Volume = 2 × 1.5 × 0.8 = 2.4 m³. Capacity = 2.4 × 1,000 = 2,400 L.
Speed combines length and time, so its units do too: km/h means kilometres per hour, and m/s means metres per second. To change km/h to m/s, convert both parts: 1 km = 1,000 m and 1 h = 3,600 s, so 1 km/h = 1,000 ÷ 3,600 m/s. In practice this means divide by 3.6 to go from km/h to m/s, and multiply by 3.6 to go back.
(a) 72 km/h = 72 ÷ 3.6 = 20 m/s.
(b) 15 m/s = 15 × 3.6 = 54 km/h.
A marathon is 42,195 m long, usually written as 42.195 km. A recipe calling for 750 mL of milk is exactly 0.75 L, or three-quarters of a standard litre carton. A farm covering 2.5 hectares spans 2.5 × 10,000 = 25,000 m².
A running track is 400 m around. How many laps make a 5 km run?
Step 1: 5 km = 5 × 1,000 = 5,000 m.
Step 2: 5,000 ÷ 400 = 12.5 laps.
Answer: 12.5 laps
A shop has 1.5 kg of flour and packs it in 250 g bags. How many bags can it fill?
1.5 kg = 1,500 g, and 1,500 ÷ 250 = 6 bags. Check: 6 × 250 g = 1,500 g. ✓
A wall is 6 m long and 2.5 m high. One litre of paint covers 10 m² for one coat. How much paint is needed for two coats?
Area: 6 × 2.5 = 15 m². Two coats: 15 × 2 = 30 m². Paint: 30 ÷ 10 = 3 litres.
The tank from Example 10 holds 2,400 L. A household uses 150 L a day. How many days will a full tank last?
2,400 ÷ 150 = 16 days.
The metre was first proposed in France in the 1790s as one ten-millionth of the distance from the North Pole to the Equator, measured along a meridian through Paris. That was an ambitious attempt to base measurement on the Earth itself, rather than an arbitrary object. Today the metre is defined using the speed of light: it is the distance light travels in a vacuum in 1/299,792,458 of a second.
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1. Divide by 1,000: 450 ÷ 1,000 = 0.45 kg.
2. 2 × 60 = 120, and 120 + 15 = 135 minutes.
3. Multiply by 10,000: 3.5 × 10,000 = 35,000 cm².
1. 3.6 × 1,000 = 3,600 m.
2. 1.5 L = 1,500 mL. 1,500 ÷ 250 = 6 glasses.
3. Area = 250 × 160 = 40,000 m². Since 1 hectare = 10,000 m², the field is 40,000 ÷ 10,000 = 4 hectares.
4. 90 ÷ 3.6 = 25 m/s. Distance in 10 s = 25 × 10 = 250 m.
5. Volume = 1.2 × 0.5 × 0.4 = 0.24 m³. Capacity = 0.24 × 1,000 = 240 L.
Students learn conversions best with real objects. Let them measure the desk in centimetres, weigh a bag of rice, and fill a jug using a 250 mL cup. Ask them to estimate first, then measure, then compare. When they convert, always ask “should the number get bigger or smaller?” Common trouble spots are area conversions and decimal time, so give extra practice with them. Everyday jobs such as cooking, shopping for fabric or paint, and planning a journey provide natural practice.
Unit conversion shows up everywhere: reading a recipe, following a doctor’s dosage instructions, understanding a weather report, buying fabric or paint by area, or reading distances on a road trip. It is also the essential first step before working with perimeter, area and volume formulas in geometry. You cannot calculate a shape’s measurements correctly if the units feeding into the formula do not match.
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