Calculate the average of ratios from up to four pairs, compare it with the ratio of sums (ratio of averages), or set your own weights for a weighted mean.

Averages each ratio equally: (a₁/b₁ + a₂/b₂ + …) ÷ number of pairs.

For a ratio 3:4 (or 3/4), enter 3 as the numerator and 4 as the denominator.

Optional settings

Average Ratio Formula

Choose a ratio of sums, an arithmetic mean of item ratios, or a custom weighted mean. These methods can give different answers. The final selected result is shown as average : 1. A ratio of sums equals a denominator-weighted mean when all denominators are positive.

Simple average ratio

rᵢ = aᵢ / bᵢ

AR = (r1 + r2 + … + rn) / n

Weighted average ratio

rᵢ = aᵢ / bᵢ

Weighted mean = Σ(rᵢ × wᵢ) / Σwᵢ

  • AR = simple average ratio
  • ARw = weighted average ratio
  • ri = decimal value of each ratio
  • ai = first number in the ratio
  • bi = second number in the ratio
  • wi = weight assigned to a ratio
  • n = number of ratios

In simple mode, each ratio counts equally. For example, 2:3 becomes 2 / 3 = 0.6667, and that decimal is averaged with the other ratio decimals.

In weighted mode, each ratio is multiplied by its weight before averaging. A ratio with a larger weight has more influence on the final average ratio.

Enter each ratio in separate numerator and denominator fields: for 2:3 or 2/3, enter 2 and 3. For a decimal such as 0.8, enter 0.8 and 1. Use the custom-weight fields only in weighted average of ratios mode. The result is displayed as AR : 1, with decimal, percent, and inverse forms also shown; the inverse is undefined for zero.

Accepted Ratio Formats and Result Meaning

  • Colon ratio 2:3: numerator 2, denominator 3; decimal value 0.6667.
  • Fraction 5/4: numerator 5, denominator 4; decimal value 1.25.
  • Decimal 0.8: numerator 0.8, denominator 1.
  • Weighted ratio 2:3 with weight 10: numerator 2, denominator 3, custom weight 10.
  • 1 : 1 means equal sides, equivalent to 100%.
  • 1.5 : 1 means the first term is 1.5 times the second, equivalent to 150%.
  • 0.5 : 1 means the first term is half the second, equivalent to 50%.

Average Ratio Examples

Example 1: Simple average ratio

Find the average ratio of 2:3, 5:4, and 7:6.

  • 2:3 = 2 / 3 = 0.6667
  • 5:4 = 5 / 4 = 1.25
  • 7:6 = 7 / 6 = 1.1667

Add the decimal values and divide by 3:

(0.6667 + 1.25 + 1.1667) / 3 = 1.0278

The average ratio is approximately 1.0278 : 1.

Example 2: Weighted average ratio

Find the weighted average ratio for these entries:

  • 2:3 with weight 10
  • 5:4 with weight 25
  • 7:6 with weight 8

Convert each ratio to a decimal and multiply by its weight:

  • 2:3 = 0.6667, so 0.6667 × 10 = 6.6667
  • 5:4 = 1.25, so 1.25 × 25 = 31.25
  • 7:6 = 1.1667, so 1.1667 × 8 = 9.3333

Divide the total weighted value by the total weight:

(6.6667 + 31.25 + 9.3333) / (10 + 25 + 8) = 47.25 / 43 = 1.0988

The weighted average ratio is approximately 1.0988 : 1.

Average Ratio Calculator FAQ

What is an average ratio?

An average ratio is the average of multiple ratio values after each ratio is converted to a decimal. For example, 2:3 is treated as 2 / 3. After all ratios are converted, the calculator finds their arithmetic mean and displays it as a ratio against 1.

When should you use a weighted average ratio?

Use a weighted average ratio when some ratios should count more than others. For example, if one ratio is based on 100 observations and another is based on 10 observations, the ratio based on 100 observations should usually receive the larger weight.

Why is the result shown as something like 1.25 : 1?

The calculator standardizes the result so the second term is 1. A result of 1.25 : 1 means the first term is 1.25 times the second term on average. The same value can also be read as 125% or inverted as 1 : 0.8.