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Simplify ratios, solve proportions and divide a total

Reduce two positive whole-number terms, share a total in that ratio, or solve a:b = x:d. Results show how a part-to-part ratio relates to percentages of the whole.

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How it works

  1. Choose Simplify ratio, Divide a total or Solve a proportion.
  2. Enter positive whole-number terms A and B. For sharing, enter the total; for a proportion, enter D in A:B = X:D.
  3. Read the simplified ratio, common factor and percentages. Copy the results to keep them.

Simplify using the greatest common divisor

The greatest common divisor (GCD) is the largest whole number that divides both terms exactly. For 12:18 it is 6, so dividing both terms by 6 gives 2:3. This tool accepts two positive safe integers whose sum is also a safe integer, up to 9,007,199,254,740,991. Decimals, negative terms and zero are outside this version’s scope.

Divide a total into ratio shares

A ratio of 3:2 has five parts in total. To share 250, one part is 250 ÷ 5 = 50; the shares are 150 and 100. Enter any positive total up to one trillion. Values retain full calculation precision, with results displayed to six decimal places; this is not a currency allocation tool that guarantees cent-rounded shares add up.

Solve a missing proportion

For A:B = X:D, X = A × D ÷ B. With 4:7 = X:21, X is 12. Enter a positive D up to one trillion. Results larger than the safe-integer ceiling are rejected; proportional results may be decimal and are rounded only for display.

Part-to-part versus part-of-total

The ratio 2:3 compares two parts with each other. The first part is 2 out of 5, or 40% of the whole; the second is 60%. A ratio of 2:3 does not mean the first part is two-thirds of the total.

Worked examples

Two-part ratios and shares computed from the same inputs
Original ratioSimplified ratioTotalFirst shareSecond share
12:182:3250100150
3:23:2250150100
16:916:91006436

Frequently asked questions

Can I simplify decimal ratios?

This version accepts positive whole-number terms. You can first multiply both decimal terms by the same power of ten: 1.2:1.8 becomes 12:18, then simplifies to 2:3. Keep the scaled values and their sum within the stated safe-integer limit.

Can I use three terms or zero?

This tool handles two positive terms. Three-part ratios and ratios containing zero are not supported.

Why do the displayed shares sometimes differ slightly from the total?

Each displayed share is rounded to six decimal places. Their internal values sum to the entered total, but separately rounded values can differ in the final decimal place.

Does simplifying change the percentages?

No. Dividing both terms by the same common factor preserves the ratio and each part’s share of the total.

Sources

Last reviewed: October 16, 2026

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