Ratio Calculator: Simplify, Scale and Divide Ratios

All three modes come from one idea: the two sides of a ratio stay in the same relationship when you multiply or divide both by the same number.

• Simplify: find the greatest common divisor (GCD) of the parts, then divide every part by it. The result has no common factor left.
• Scale: new ratio = (a × k) : (b × k), where k is your scale factor.
• Divide an amount: share of part i = amount × part_i ÷ (sum of all parts).

Simplify 12:18. The GCD of 12 and 18 is 6. Divide both sides by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12:18 simplifies to 2:3.

Divide $100 by 2:3. Total parts = 2 + 3 = 5. Each part is worth $100 ÷ 5 = $20. The shares are 2 × $20 = $40 and 3 × $20 = $60, which add back to $100.

Pick the mode that matches your task, enter the numbers, and press Calculate. The calculator shows each step so you can check the working, not just the answer.

Step by step

1. Choose a mode. Simplify reduces a ratio; Scale grows or shrinks it; Divide splits an amount.
2. Enter the ratio parts. Decimals are fine — the calculator clears them before finding the GCD.
3. Add the extra input. A scale factor for Scale mode, or the amount (and optional third part) for Divide mode.
4. Press Calculate. You get the result plus the GCD or the per-part value used.

Ratios and fractions

A ratio is closely related to a fraction: 2:3 expresses the same relationship as the fraction 2/3, which is why dividing by a ratio uses the same total-parts idea as adding fractions with a common denominator. If you need the fraction arithmetic itself, a fraction calculator handles adding, subtracting and simplifying fractions step by step.

The greatest common divisor is the largest whole number that divides every part of the ratio. Dividing by the GCD is the fastest route to simplest form because it removes all common factors in one step.

Common simplifications

Finding a missing value

When you know three of the four numbers in a proportion such as 3:4 = x:12, cross-multiply: 4x = 3 × 12 = 36, so x = 9. The diagram above shows the two multiplication paths that make "cross" multiplication visual.

Splitting by ratio keeps every share proportional to its part. A 2:3:5 split of 100 servings gives 20, 30 and 50 — ten servings per part, since there are 10 parts in total.

Where this gets used

Shares as percentages

Sometimes you want each share as a percentage of the whole instead of a raw amount. A share of $40 from $100 is 40%, which is just the part divided by the total parts times 100. A percentage calculator converts any share to a percentage instantly if you prefer working that way.

Scaling multiplies every part by the same factor, so the relationship never changes. Doubling a 2:3 paint mix to 4:6 gives twice as much paint with the same colour.

Scaling reference

Common mistakes

The classic error is scaling only one side — doubling 2:3 to 4:3 changes the mixture entirely. Another is forgetting that scaled ratios can be simplified again: 4:6 is correct but 2:3 is cleaner. Always scale every part, then simplify the result.