Unit conversions

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Unit guide

For this conversion

Common science units
Length
m; mm, cm, km
Mass
kg; g, mg
Time
s; min, h
Temperature
°C
Area / volume
m² / m³; cm² / cm³
Force / energy / power
N / J / W
Current / potential difference / resistance
A / V / Ω
Speed / acceleration
m/s / m/s²
Density
kg/m³ or g/cm³
Mass concentration
g/dm³
Rate of reaction
g/s or cm³/s
Gravitational field strength
N/kg
Spring constant
N/m
Specific latent heat
J/kg
Specific heat capacity
J/(kg °C)
Frequency / electric charge
Hz / C
Combining units
“Per” means divide

Some quantities combine two measurements. Speed tells you how much distance is travelled each second.

12 m4 s=3 m/s

Divide the numbers and divide the units. m/s means metres per second. The unit before the slash is on top.

Rates use an amount per second

A reaction can be measured using the volume of gas made, or the mass lost, in a measured time.

20 cm³5 s=4 cm³/s
Mass ÷ timeg/s
Gas volume ÷ timecm³/s

Keep the cubic symbol when you divide a volume by time. cm³/s is a volume each second; cm/s is a length each second.

Mass per volume

Density describes mass per volume of a material. Mass concentration describes the mass of solute per volume of solution.

Density: kg ÷ m³kg/m³
Density: g ÷ cm³g/cm³
Mass concentration: g ÷ dm³g/dm³

For example, 6 g of solute in 0.5 dm³ of solution gives 6 ÷ 0.5 = 12 g/dm³. Use the units given, or convert to the units required.

Dividing by seconds twice

Acceleration tells you how quickly velocity changes. The change in velocity already has the unit m/s.

6 m/s3 s=2 m/s²

(m/s) ÷ s = m/(s × s) = m/s². Here the velocity changes by 2 m/s each second. The metres are not squared.

Units can multiply or cancel

Follow the operation in the equation. Multiplying two units does not always leave both in the answer.

kg × Nkg=N
N × m = N m = J

In kg × N/kg, the kg units cancel. In force × distance, N × m gives newton metres. For work done, 1 N m = 1 J.

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