Ratio Scale Examples: What It Is, Formula and Worked Example

A ratio scale is a level of measurement with equal intervals between values and a true zero, so a value of zero means none of the quantity and statements such as “four times as much” are valid. Body mass in grams, length in metres, duration in seconds and temperature in kelvin are ratio-scale variables; temperature in degrees Celsius is not. This page defines the scale, gives the ratio formula with a worked calculation, shows a true-zero test against near-miss variables, and ends with reporting and software snippets. For the wider family of quantitative variables, see quantitative data examples.

What is a ratio scale?

A ratio scale is the highest of the four classic levels of measurement (nominal, ordinal, interval, ratio). OpenStax’s Introductory Statistics 2e (section 1.3) describes ratio data as data where “there is a minimum value and ratios can be calculated.” Interval data, by contrast, allow differences between values to be calculated but have “no minimum or ‘zero’ value.”

Two properties define the scale. First, equal steps mean equal amounts anywhere on the scale, so the difference between 10 g and 20 g equals the difference between 40 g and 50 g. Second, zero is a true, non-arbitrary origin: 0 g of a sample is no sample. The second property is what separates ratio from interval data and what makes multiplication and division of values meaningful.

Ratio scale formula (a / b)

There is no single named formula for the scale itself; the defining operation is the ratio of two measurements:

r = a / b

• a is the measurement of the first object or case, in any unit of a ratio-scale variable.
• b is the measurement of the second object or case, in the same unit, with b greater than zero.
• r is the ratio: “a is r times b”. It has no unit, and it stays the same if both values are converted to another unit by a pure rescaling (grams to kilograms, for example).

That last property is the practical test. On a ratio scale, converting units multiplies every value by the same constant, so r does not change. On an interval scale the conversion adds an offset as well, which is why ratios of Celsius values change when you switch to kelvin.

Ratio scale examples with a true-zero test

Ask one question: does a value of zero mean “none of the thing being measured”? If yes, the variable is ratio-scale. If zero is a convenient label for a point on a scale, it is not.

Variable	Zero means	Scale
Body mass in grams	No mass	Ratio
Length in metres	No length	Ratio
Duration in seconds	No time elapsed	Ratio
Number of phone calls in a day	No calls	Ratio
Temperature in kelvin	Absolute zero	Ratio
Temperature in degrees Celsius	The 0 point is a convention (273.15 K)	Interval
Calendar year	A conventional starting point, not “no time”	Interval

Each row applies the same test. Mass, length, duration and counts have a physical zero that means none. The Celsius and kelvin rows are explained in the next section. A year number is a label on a time axis whose origin was chosen by convention, so a year of 0 does not mean no time.

Ratio vs interval scale

The difference shows up in the arithmetic. The NIST page on the kelvin gives “0 K = -273.15 degrees C = -459.67 degrees F” and describes the Kelvin scale as starting at absolute zero. Celsius therefore places its zero at a point that is 273.15 K above absolute zero.

Take two room temperatures, 20 °C and 40 °C. Is 40 °C “twice as hot”?

• Convert to kelvin by adding 273.15: 20 + 273.15 = 293.15 K and 40 + 273.15 = 313.15 K.
• Ratio in kelvin: 313.15 / 293.15 = 1.068, about 1.07.
• Ratio of the Celsius numbers: 40 / 20 = 2.

The two ratios disagree, so the Celsius ratio carries no physical meaning. The Celsius difference (20 degrees) is valid, which is why Celsius is an interval scale. For more on that side of the divide, see the types of variables entry and the categorical variable examples guide.

Worked example with real numbers

Illustrative numbers (not from a study): four reagent samples weighed in grams, a ratio-scale variable.

Sample	Mass (g)	Deviation from mean	Squared deviation
A	12.5	-18.75	351.5625
B	50.0	18.75	351.5625
C	25.0	-6.25	39.0625
D	37.5	6.25	39.0625

1. Ratio statement: B / A = 50.0 / 12.5 = 4.0, so sample B is four times the mass of sample A. Converting to kilograms (0.0500 / 0.0125) still gives 4.0.
2. Mean: (12.5 + 50.0 + 25.0 + 37.5) / 4 = 125.0 / 4 = 31.25 g.
3. Sum of squared deviations: 351.5625 + 351.5625 + 39.0625 + 39.0625 = 781.25.
4. Sample variance: 781.25 / (4 – 1) = 260.42 g².
5. Sample standard deviation: √260.42 = 16.14 g.

The same steps are laid out in how to find sample variance. OpenStax makes the same point with exam scores: of 80, 68, 20 and 92, “80 is four times 20.” We use masses here so the zero is physical (no mass), not a scoring convention.

Interpretation: what a ratio-scale result lets you say

Result	Valid on a ratio scale	Example from above
Difference (a – b)	Yes	B is 37.5 g heavier than A
Ratio (a / b)	Yes	B is 4.0 times A
Mean and standard deviation	Yes	31.25 g and 16.14 g
Value of zero	Means none	0 g is no sample

Everything allowed on an interval scale (differences, means, standard deviations) remains allowed; ratios are the addition.

Assumptions and common mistakes

• Treating Celsius or Fahrenheit as ratio data. “40 °C is twice 20 °C” fails the kelvin check above. Convert to kelvin first.
• Treating ordinal scores as ratio data. A rating of 4 is not twice a rating of 2 unless the scale has equal steps and a true zero.
• Dividing by zero or near-zero. A ratio a / b needs b greater than zero; a b near zero makes r unstable.
• Mixing units. Both measurements must be in the same unit before dividing.
• Confusing the scale with the data type. Ratio-scale data can be discrete (counts) or continuous (masses, lengths).

How to report a ratio-scale variable (APA example)

APA style (7th edition) uses the symbols M and SD for the mean and standard deviation, sets statistical symbols in italics, and reports means and standard deviations to two decimals. Using the worked example: “Sample mass was M = 31.25 g (SD = 16.14 g, n = 4).” A ratio statement is written in plain language with the numbers shown: “The heaviest sample (50.0 g) was four times the mass of the lightest (12.5 g).”

How to calculate it in Excel, R or Python

Excel

Ratio:   =B2/A2
Mean:    =AVERAGE(A2:A5)
SD:      =STDEV.S(A2:A5)

R

x <- c(12.5, 50.0, 25.0, 37.5)
x[2] / x[1]   # 4
mean(x)       # 31.25
sd(x)         # 16.13743

Python

import statistics as st
x = [12.5, 50.0, 25.0, 37.5]
print(x[1] / x[0])     # 4.0
print(st.mean(x))      # 31.25
print(st.stdev(x))     # 16.13743...

For a temperature ratio, convert first: (40 + 273.15) / (20 + 273.15) returns 1.068.

FAQ

What is a ratio scale in simple terms?

It is a measurement scale with equal intervals and a true zero, so you can say one value is a certain number of times another. Mass, length and time are the standard examples.

What is the ratio scale formula?

The defining comparison is r = a / b, where a and b are two measurements in the same unit and b is greater than zero. The result is unit-free and is unchanged by converting both values to another unit.

Is temperature a ratio scale?

Only in kelvin. The Kelvin scale starts at absolute zero (0 K = -273.15 °C), so ratios of kelvin values are meaningful; ratios of Celsius or Fahrenheit values are not.

What is the difference between interval and ratio scales?

Both have equal intervals, but only the ratio scale has a true zero. That is why differences are valid on both, and ratios on the ratio scale alone.

Sources

All links checked 29 October 2026.

• OpenStax, Introductory Statistics 2e, section 1.3 “Frequency, Frequency Tables, and Levels of Measurement”: https://openstax.org/books/introductory-statistics-2e/pages/1-3-frequency-frequency-tables-and-levels-of-measurement
• National Institute of Standards and Technology, “Kelvin: Introduction”: https://www.nist.gov/si-redefinition/kelvin-introduction
• American Psychological Association, “Numbers and Statistics Guide” (7th edition): https://apastyle.apa.org/instructional-aids/numbers-statistics-guide.pdf