TinySandyFree Online Tools

Ratio Calculator

A ratio calculator for four everyday jobs: reduce a ratio such as 24 : 36 : 60 to its simplest whole-number form, find the missing number in a proportion like 3 : 5 = 12 : ?, split a total such as 1,000 between people in the ratio 2 : 3 : 5, or express a ratio as percentages. The working is written out in plain steps.

Math Runs in your browser

Work with Ratios

Exact fraction arithmetic is used throughout. Decimal terms are scaled to whole numbers before simplifying (1.5 : 2.5 becomes 3 : 5). In the proportion mode, fill three of the four boxes and leave one empty.

Two to six non-negative numbers separated by : or / or the word “to”, commas or spaces. Decimals are fine.

How to Use the Ratio Calculator

  1. Pick what you want to do.
  2. Type the ratio (or fill A, B, C, D leaving one blank; or enter the total to share).
  3. Press Calculate.
  4. Read the result and the steps beneath it.

About This Tool

Students with ratio and proportion homework, cooks scaling recipes, designers keeping an aspect ratio, and anyone splitting costs or profits in fixed shares.

Input: Numbers  ·  Output: Ratio.

Features and Limitations

Features

  • Simplifies ratios with two to six terms, including decimals.
  • Solves for any one missing term of A : B = C : D.
  • Shares a total in a ratio with exact amounts.
  • Gives percentages and fractions of the whole.
  • Explains each step.

Limitations

  • Terms must be zero or positive numbers; negative ratios are not supported.
  • A term that would make you divide by zero (for example solving for D when A is 0) is refused with an explanation.
  • When the shares of a total do not divide evenly they are rounded for display, so the displayed parts can differ from the total by a rounding amount.
  • At most six terms are supported.
  • Results are computed in your browser; nothing you enter is sent to a server.

Example

24 : 36 : 60 simplifies to 2 : 3 : 5. In 3 : 5 = 12 : D, D = 5 × 12 ÷ 3 = 20. Sharing 1,000 in the ratio 2 : 3 : 5 gives 200, 300 and 500. The ratio 2 : 3 is 40% and 60%.

Frequently Asked Questions

How do I simplify a ratio?

Divide every term by their greatest common divisor (GCD). For 24 : 36 : 60 the GCD is 12, so the ratio is 2 : 3 : 5. For decimals, multiply all terms by a power of ten first so they become whole numbers.

How do I solve a proportion A : B = C : D?

Cross-multiply: A × D = B × C. So D = B × C ÷ A, C = A × D ÷ B, B = A × D ÷ C and A = B × C ÷ D. Check the result by confirming the two cross products are equal.

How do I divide an amount in a given ratio?

Add the ratio terms to get the number of parts, divide the total by that number, then multiply by each term. To split 1,000 in 2 : 3 : 5: 1,000 ÷ 10 = 100 per part, giving 200, 300 and 500.

How do I turn a ratio into a percentage?

Each term ÷ sum of all terms × 100. For 2 : 3 the sum is 5, so the parts are 2/5 = 40% and 3/5 = 60%.

What does 1 : n mean?

It restates a two-term ratio with the first term as 1, for example 3 : 5 is 1 : 1.6667, which makes it easy to compare scales or aspect ratios.

Related Tools

More like this: all Math tools, all Calculators tools or the TinySandy home page.