Units let us know what property is being measured, and they tell us the magnitude scale.
Metric units follow powers of ten. There are 100 cm in a meter, and 1000 mm in a meter.
English units have less predictable relationships. There are 3 feet in a yard, and 12 inches in a foot, and 36 inches in a yard.
Metric Units
The metric system was designed to be a unified and rational system of measures.
The metric system improves calculation, communication, and conversion.
Amazingly, it has been adopted by almost every country on Earth.
Annoyingly, United States have chosen to not fully adopt the metric system, but
the American sciences do use metric. We use metric units on this site.
The metric system defines all units from seven base units. The base units come from measuring physical constants.
For example, the meter is defined as the distance light travels in (1 / 299 792 458) seconds.
Quantity
Name
Symbol
time
second
s
length
meter
m
mass
kilogram
kg
current
ampere
A
temperature
kelvin
K
amount
mole
mol
light intensity
candela
cd
Derived units are combinations of these base units.
For example, velocity is combination of length divided by time (m/s).
Quantity
Name
Symbols
area
meters squared
m²
volume
meters cubed
m³
velocity
meters per seconds
m/s
acceleration
meters per seconds squared
m/s²
momentum
kilogram meters per seconds
kg m/s
Some derived units get a special abbreviation normally written as a capital letter.
For example, the unit of force is N, but it stands for kg m/s².
Quantity
Name
Abbreviation
Symbols
force
newton
N
kg m/s²
energy
joule
J
kg m²/s²
power
watt
W
kg m²/s³
frequency
hertz
Hz
1/s
volume
liter
L
10⁻³ m³
Metric Prefixes
We use metric prefixes to indicate multiplication or division by powers of ten.
For example we can replace 1000 with the letter "k".
Example: How many meters is 10 Mm?
solution10Mm=10.000000.m=10000000m
Example: How many seconds is 10 μs?
solution10μs=0.000010.0s=0.00001s
Nonmetric Units
Converting outside the metric system is more complex.
Other unit systems don't always use powers of ten, so we can't simply move the decimal left or right.
To convert we need to multiply by a conversion fraction.
Build a conversion fraction.
Put the old unit on the bottom of the fraction.
Put the new unit on top of the fraction.
Find out how two numbers are equal.
Add numbers to the top and bottom of the fraction so that they are equal.
Multiply the number you are converting by the conversion fraction.
The old unit should cancel to leave just the new unit.
Let's convert 50 minutes into seconds.
50min→s
In order to cancel minutes we want to build a fraction with minutes on top and the seconds on the bottom.
50min(mins)
Our fraction can't change the actual value, so it must be equal to one. The top and bottom of the fraction must equal each other.
Example: Convert 50 minutes into hours.
solution50min→hour50min(60min1hour)6050hour0.833hour
Example: A marathon is 26.2 miles. How far is a marathon in kilometers?
(1 mile = 1.6 kilometers)
solution26.2mile(1mile1.6km)=41.92km
Example: I'm 6 feet and 1 inch tall. How many meters tall am I?
solutionft→inches6ft+1in6ft(1ft12in)+1in72in+1in73in inches→metersa google search returns: 1m=39.37in73in(39.37in1m)73(39.371m)1.85m