Units in Equations

Here are some common Units in Physics:

Property Name Symbol
Length meter m
Mass kilogram kg
Time second s
Force Newton N
Energy Joule J
Per second Hertz Hz

And we put Metric Number Prefixes in front of the symbol to write larger or smaller values:

Name The Number Prefix Symbol
trillion 1,000,000,000,000 tera T
billion 1,000,000,000 giga G
million 1,000,000 mega M
thousand 1,000 kilo k
hundred 100 hecto h
ten 10 deka da
unit 1    
tenth 0.1 deci d
hundredth 0.01 centi c
thousandth 0.001 milli m
millionth 0.000 001 micro µ
billionth 0.000 000 001 nano n
trillionth 0.000 000 000 001 pico p


Now ... how do we us them in equations?

First: it is common to just use the symbol (such as km for kilometers).

Adding and Subtracting

Use the same units when we add or subtract!


Example: Sam is designing a new table. The old table is 2 m long. The new table should be 200 mm longer:

2 m + 200 mm = ?

The units need to be the same!

We can choose m (meters) or mm (millimeters).

Let's choose mm. 1 m is 1000 mm, so:

2000 mm + 200 mm = 2200 mm

Or we could choose m:

2 m + 0.2 m = 2.2 m

Multiplying and Dividing

When multiplying put the units next to each other

When dividing put the unit after "/"

Like this:

Example: Alex walks 100 m in 80 seconds, what average speed is that?

Speed is distance/time

Speed = 100 m 80 s = 1.25 m/s

100 divided by 80 is 1.25, and m divided by s is m/s

ball kick

Example: Hunter kicks a soccer ball. It goes from 0 to 32 m/s in 0.1 seconds. What is the acceleration?

Acceleration is:

Change in Velocity (m/s) Time (s)

Put in the values we know:

Acceleration = 32 m/s − 0 m/s 0.1s = 320 m/s2

The "m/s" becomes "m/s /s" which is m/s2

Sometimes there is a special unit that is made up of other units:

Example: The soccer ball weighs 0.4 kg, what is the force of Hunter's kick?

We can use Newton's Second Law of Motion:

F = ma

The mass m = 0.4kg,
and we already calculated the acceleration: a = 320 m/s2

F = 0.4 kg × 320 m/s2

F = 128 kg m/s2

1 Newton (N) is the usual measure of force, and equals 1 kg m/s2, so:

F = 128 N