Unit conversions — standard and compound

Unit conversion appears in OCR J560 every series, from Foundation Paper 1 (simple length conversions) to Higher Paper 6 (compound units like kg/m³ or m/s²). Get a feel for "× and ÷ by powers of 10" and "what to do with squared/cubed units".

Standard units (length, mass, time, capacity)

Quantity	Common conversions
Length	1 km = 1000 m; 1 m = 100 cm; 1 cm = 10 mm
Mass	1 tonne = 1000 kg; 1 kg = 1000 g; 1 g = 1000 mg
Capacity	1 litre = 1000 ml; 1 ml = 1 cm³
Time	1 hr = 60 min; 1 min = 60 s; 1 hr = 3600 s

To convert from a smaller unit to a larger unit, divide. Larger to smaller: multiply.

Area conversions (squared units)

The trick: when units are squared, the conversion factor is squared.

• 1 m = 100 cm, so 1 m² = 100 × 100 = 10 000 cm².
• 1 km = 1000 m, so 1 km² = 1000 × 1000 = 1 000 000 m².

Volume conversions (cubed units)

• 1 m = 100 cm, so 1 m³ = 100³ = 1 000 000 cm³.
• 1 cm³ = 1 ml; 1 m³ = 1000 litres.

Compound units

Compound units express one quantity per another.

Quantity	Unit	Example conversion
Speed	m/s, km/h, mph	1 m/s = 3.6 km/h
Density	g/cm³, kg/m³	1 g/cm³ = 1000 kg/m³
Pressure	N/m² (Pa), N/cm²	1 N/cm² = 10 000 N/m²

Speed: m/s ↔ km/h

To convert m/s to km/h: × 3.6. To convert km/h to m/s: ÷ 3.6.

Why? In 1 hour (3600 s), 1 m/s travels 3600 m = 3.6 km. So 1 m/s = 3.6 km/h.

Density: g/cm³ ↔ kg/m³

× 1000 going g/cm³ → kg/m³ (because 1 g/cm³ = 1000 kg/m³).

OCR mark scheme conventions

• B1 for a correct conversion as a stand-alone step.
• M1 for substituting a converted value into a formula.
• A1 cao for the final numerical answer with correct units.
• Working in mixed units almost always loses the A1 even if the number is right.