Ratio Scale
Definition

A ratio scale is a scale (of measurement) created by units of equal size (like an interval scale) with the added condition that "zero" is not arbitrary.


When dealing with a ratio scale, the difference between any two values can be calculated by using subtraction.

When dealing with a ratio scale, the ratio of any two values can be calculated by using division.


Some examples of variables that use ratio scales would be distance, speed, weight, temperature (Kelvin), etc.


Example (Speed)

Physics defines speed as "distance traveled divided by the time of travel". When looking at "speed", zero means that an object is at rest (the distance traveled is zero). The interval size is chosen based on the units of distance and time. In the metric system, the speed of a vehicle is measured in kilometres per hour (km/h). In the Imperial system speed of a vehicle is measured in miles per hour (mph).


A comparison of the two ratio scales is shown in the illustration below.


Comparison of Metric and Imperial scales for speed

Equal differences in any two speeds on one scale will result in equal differences on the other scale.

Comparison of speed differences on Metric and Imperial scales

Note that 35 km/h - 20 km/h = 70 km/h - 55 km/h (both are a difference of 15 km/h).

Note that 21.75 mph - 12.43 mph = 43.50 mph - 34.18 mph (both are a difference of 9.52 mph).


A difference of 15 km/h is equivalent to a difference of 9.52 mph, regardless of where you are on either scale.


Divider Line

The ratio of any two speeds on one scale will be equivalent to the ratio of two equivalent speeds on another scale.

Ratio comparison of speeds on the Metric and Imperial scales

The ratio of 84 km/h to 42 km/h is 2.

The ratio of 52.206 mph to 26.103 mph is also 2.


Twice as fast on either scale has the same meaning since the location of zero represents the same thing on both scales.


If it is desired to know how how fast it is if it is twice as fast as 42 km/h, multiply 42 km/h by 2.

If it is desired to know how how fast it is if it is twice as fast as 26.103 mph, multiply 26.103 mph by 2.


Canadian cars usually display speed in both Metric and Imperial units, as illustrated in the sample display below.

Canadian car speedometer example