Ratio Simplifier Calculator
Reduce any ratio of 2 or 3 numbers to its simplest form. Enter 8 and 12 to get 2:3, or 6, 9 and 12 to get 2:3:4 — with the GCD steps, decimal forms and equivalent ratios shown.
- Your input
- GCD
- Decimal a ÷ b
- Decimal b ÷ a
- Your input
- GCD
- Unit form (a = 1)
Worked examples
GCD of 48 and 18:
- 48 ÷ 18 = 2 remainder 12
- 18 ÷ 12 = 1 remainder 6
- 12 ÷ 6 = 2 remainder 0
- GCD = 6
Stage 1: GCD(6, 9) = 3. Stage 2: GCD(3, 12) = 3. Divide all three terms by 3 → 2:3:4 (unit form: 1 : 1.5 : 2).
Not what you're looking for?
This tool only reduces ratios to simplest form. Related calculators:
- Percentage calculator — "X is what percent of Y", percent of a number, percent change.
- Percent to ratio calculator — convert 25% to 1:3 and back.
- Decimal to ratio calculator — turn 0.75 into 3:4.
- Aspect ratio calculator — screen and image ratios such as 16:9.
- Golden ratio calculator — proportions based on φ (1.618…).
Frequently asked questions
How do you simplify a ratio?
Find the greatest common divisor (GCD) of all terms, then divide every term by it. Example: 2:3 is the simplest form of 8:12, because 8 and 12 share GCD 4, and 8 / 4 = 2, 12 / 4 = 3.
What is 8:12 in simplest form?
8:12 in simplest form is 2:3. Divide both terms by their GCD, 4: 8 / 4 = 2 and 12 / 4 = 3, and 2 and 3 share no common divisor.
How does the Euclidean algorithm find the GCD of a ratio?
Divide the larger term by the smaller and keep the remainder, then repeat with the divisor and remainder until the remainder is 0. For 48:18: 48 ÷ 18 = 2 remainder 12; 18 ÷ 12 = 1 remainder 6; 12 ÷ 6 = 2 remainder 0; GCD = 6. The last non-zero divisor, 6, is the GCD, so 48:18 simplifies to 8:3.
How do you simplify a ratio of 3 numbers?
Find the GCD in two stages: first GCD(a, b), then GCD of that result with c, and divide all three terms by the final GCD. Example: 6:9:12 has GCD(6, 9) = 3 and GCD(3, 12) = 3, so it simplifies to 2:3:4. As a unit ratio that is 1 : 1.5 : 2.
How do you simplify a ratio with decimals?
Scale every term to a whole number first, then simplify exactly. Example: 1.5:2.5 becomes 3:5 after multiplying by 2, and 0.25:0.75 becomes 1:3 after multiplying by 4. This calculator does the scaling with exact fraction math, so no rounding error sneaks in.
What is 15:25 in simplest form?
15:25 in simplest form is 3:5. Both terms share GCD 5: 15 / 5 = 3 and 25 / 5 = 5.
What are equivalent ratios?
Equivalent ratios express the same relationship with different numbers: multiply or divide every term by the same value. 2:3 is equivalent to 4:6, 6:9 and 8:12. This calculator shows the x2, x3 and x4 equivalents of every simplified ratio.
How do you write a ratio as a decimal?
Divide the first term by the second. 2:3 as a decimal is 2 / 3 = 0.666667. The reciprocal, 3 / 2 = 1.5, tells you how many times the second term fits in the first.
What is 2:4:6 in simplest form?
2:4:6 in simplest form is 1:2:3. All three terms share GCD 2. Written with the first term as 1, it is 1 : 2 : 3.
Can a ratio contain zero?
Yes, as long as not every term is zero. 0:5 simplifies to 0:1, meaning the first part is empty. A ratio like 0:0:0 has no simplest form and is rejected.
What is 0.25:0.75 in simplest form?
0.25:0.75 in simplest form is 1:3. Multiply by 4 to get 1:3, which is already in lowest terms since 1 and 3 share only GCD 1.
What is the difference between a ratio, a fraction and a percent?
A ratio a:b compares two quantities; the fraction a/(a+b) is the first part's share of the total; a percent is that share times 100. This tool only simplifies ratios. For "X is what percent of Y" use a percentage calculator, for percent to ratio conversion use a percent-to-ratio calculator, and for decimal to ratio use a decimal-to-ratio calculator.
Free tool by NRTechStudio