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Metric and Imperial: Height, Weight and Distance

Goal Switch between metric and imperial units for height, weight and distance, quickly in your head or exactly with a calculator.

WHY THIS MATTERS

Most of the world uses the metric system (metres, kilograms), but the United States uses imperial units (feet, pounds, miles), and the UK uses a mix: road signs in miles, body weight often in stones. Online shopping, travel, job forms, medical forms and sports all make you switch between the two.

KEY WORDS

Metric system: millimetres (mm), centimetres (cm), metres (m), kilometres (km), grams (g) and kilograms (kg). Every step is a multiple of 10.
Imperial system: inches (in), feet (ft), yards (yd), miles (mi), ounces (oz), pounds (lb) and stones (st).
Conversion factor: the number you multiply or divide by to change units.

METRIC STEPS JUST MOVE THE DECIMAL POINT

10 mm = 1 cm
100 cm = 1 m
1,000 m = 1 km
1,000 g = 1 kg

Example: 2.5 m = 250 cm. And 750 g = 0.75 kg.

THE KEY CONVERSION FACTORS

Length and height:

1 inch = 2.54 cm (exactly)
1 foot = 12 inches = 30.48 cm
1 metre = about 3.28 feet, or 39.4 inches
1 yard = 3 feet = 0.91 m

Distance:

1 mile = 1.609 km
1 km = 0.621 miles

Weight:

1 kg = 2.205 lb
1 lb = 0.454 kg
1 stone = 14 lb = 6.35 kg

Key pairs to remember: 1 inch is 2.54 centimetres, 5 miles is about 8 kilometres, 1 kilogram is about 2.2 pounds, and 1 foot is about 30.5 centimetres.

WHICH WAY DO I MULTIPLY OR DIVIDE

A simple check: when you change to a smaller unit, you get a bigger number. Centimetres are smaller than inches, so inches to centimetres means the number gets bigger: multiply by 2.54. Centimetres to inches means the number gets smaller: divide by 2.54.

QUICK MENTAL ESTIMATES

Kilograms to pounds: double it and add 10%. 70 kg → 140 + 14 = 154 lb (exact: 154.3 lb).
Pounds to kilograms: halve it and take off 10%. 200 lb → 100 − 10 = 90 kg (exact: 90.7 kg).
Miles to kilometres: multiply by 1.6. 50 miles → 80 km.
Kilometres to miles: multiply by 0.6. 100 km → 60 miles (exact: 62.1 miles).
Handy pairs to remember: 5 miles ≈ 8 km, and 8 miles ≈ 13 km.

HEIGHT FEET AND INCHES TO CENTIMETRES

Turn everything into inches: feet × 12, plus the extra inches.
Multiply by 2.54.

Example: 5 feet 10 inches = (5 × 12) + 10 = 70 inches. Then 70 × 2.54 = 177.8 cm, so about 178 cm.

Going back: 165 cm ÷ 2.54 = 65 inches. Then 65 ÷ 12 = 5 remainder 5, so 5 feet 5 inches.

SPEED

100 km/h = about 62 mph
60 mph = about 97 km/h
Speed conversions use the same factors as distance: multiply mph by 1.609 to get km/h.

THE CONVERSION-FACTOR METHOD (FOR TRICKY CHAINS)

Write each conversion as a fraction that equals 1, then multiply. Units on the top and bottom cancel out, so you can check you haven't flipped anything.
Example: how many centimetres in 3 yards?

3 yards × (3 feet ÷ 1 yard) = 9 feet
9 feet × (12 inches ÷ 1 foot) = 108 inches
108 inches × (2.54 cm ÷ 1 inch) = 274.32 cm

REAL-LIFE CASE STUDY DAVID FILLS IN A VISA MEDICAL FORM

The form asks for height in centimetres and weight in kilograms. David knows he is 6 feet 1 inch and 185 lb.

Height: (6 × 12) + 1 = 73 inches. Then 73 × 2.54 = 185.4 cm, so he writes 185 cm.
Weight: 185 × 0.454 = 84 kg (exact: 83.9 kg).

Funny coincidence: his height in centimetres and his weight in pounds are both about 185.

PRACTICE

Complete the sentences.

Drag a word into each gap, or tap a word and then tap the gap.

One foot is inches.
One inch is cm.
One stone is pounds.
A distance of 50 miles is about km.
One metre is cm.

✓ Check Your Understanding

Pick one answer for each question. You'll see the explanation straight away.

1. Someone is 5 feet 8 inches tall. What is that in centimetres, to the nearest whole number?

5 feet 8 inches = (5 × 12) + 8 = 68 inches. Then 68 × 2.54 = 172.7 cm, which rounds to 173 cm. (177 cm comes from mistakenly treating "5 feet 8" as 5.8 feet, and 147 cm from treating it as 58 inches.)

2. A suitcase limit is 23 kg. Roughly what is that in pounds?

Double 23 kg to get 46, then add 10% (4.6) to get about 51 lb. The exact answer is 23 × 2.205 = 50.7 lb. (46 is a common answer from doubling only.)

3. A road sign in the UK says 30 miles. About how far is that in kilometres?

Multiply miles by 1.6: 30 × 1.6 = 48 km (exact: 48.3 km). Miles are longer than kilometres, so the number of kilometres must be bigger. (19 km comes from multiplying by 0.621, which is the factor for going the other way, from km to miles.)

4. A TV screen is 55 inches across. How many centimetres is that?

Inches to centimetres means multiply by 2.54: 55 × 2.54 = 139.7 cm. Centimetres are smaller than inches, so the number gets bigger. (22 cm comes from dividing instead of multiplying.)

5. A friend says they weigh 11 stone. How much is that in kilograms?

11 stone × 14 = 154 lb, and 154 × 0.454 = 69.9 kg, so about 70 kg. (154 is the weight in pounds, not kilograms.)

You got out of 5. Excellent work! Read the explanations above, then try again.

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