Percent to Ratio Calculator
Convert percent to ratio, ratio to percent, and slope percent to ratio grade with exact integer math. No rounding, no estimates.
Tip: enter a number for percent to ratio grade, or a:b to convert a ratio grade back to slope percent.
Worked examples
20 : 80, divide by GCD 20
25 : 75, divide by GCD 25
50 : 50, divide by GCD 50
75 : 25, divide by GCD 25
1 ÷ (1 + 3) × 100
3 ÷ (3 + 1) × 100
10 : 100, divide by GCD 10
5 : 100, divide by GCD 5
Common percent to ratio table (1–99)
| Percent | Ratio | Percent | Ratio | Percent | Ratio |
|---|
Scope boundary
This tool converts percent ↔ ratio and slope grade with exact math. Related but different tools:
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- Gear ratio calculator (nrtechstudio tool #425): mechanical gear teeth ratios, not percent conversion.
- Aspect ratio calculator: screen and image dimensions (16:9 etc.), not percent to ratio.
- Golden ratio calculator: the design proportion 1.618, not percent conversion.
- Decimal to ratio calculator (nrtechstudio tool #872): decimal-first conversions; its percent tab expresses the fraction (25% as 1:4), while this tool uses the canonical part-to-rest convention (25% as 1:3) plus slope grades.
Frequently asked questions
How do you convert a percent to a ratio?
Write the percent as a ratio of the part to the rest: P% becomes P : (100 - P), then divide both terms by their greatest common divisor. Example: 25% becomes 25:75, and 25 and 75 share GCD 25, so the simplified ratio is 1:3.
What is 20% as a ratio?
20% as a ratio is 1:4. Write 20 : 80 and divide both terms by their GCD, 20, to get 1:4.
What is 75% as a ratio?
75% as a ratio is 3:1. Write 75 : 25 and divide both terms by their GCD, 25, to get 3:1.
What is 50% as a ratio?
50% as a ratio is 1:1. Write 50 : 50 and divide by 50 to get 1:1, meaning the two parts are equal.
Why is 25% equal to 1:3 and not 1:4?
A ratio a:b means the first part is a out of a+b total parts, so 25% = 25:75 = 1:3. The form 1:4 is the fraction 1/4 written with a colon; it expresses part-to-whole, not part-to-rest. Both conventions exist on the web, but part-to-rest (25% = 1:3) is the standard used in school worksheets and dedicated percent-to-ratio calculators.
How do you convert a ratio back to a percent?
Add the terms to get the total, then divide the first term by the total and multiply by 100: percent = 100 x a / (a+b). Example: 1:3 becomes 1 / (1+3) x 100 = 25%.
What is 1:4 as a percent?
1:4 as a percent is 20%. Compute 1 / (1+4) x 100 = 20%.
How do you convert a slope percent to a ratio grade?
Write the slope as rise over run: s% becomes s : 100, then simplify with the GCD. Example: a 10% slope becomes 10:100, and dividing by GCD 10 gives the grade 1:10.
What is a 5% slope as a ratio?
A 5% slope as a ratio grade is 1:20. Write 5 : 100 and divide both terms by their GCD, 5, to get 1:20, meaning 1 unit of rise for every 20 units of run.
How do you convert a ratio grade back to slope percent?
Divide the rise by the run and multiply by 100: slope = 100 x a / b. Example: a 1:10 grade becomes 100 x 1 / 10 = 10%.
What is a 12% slope as a ratio?
A 12% slope as a ratio grade is 3:25. Write 12 : 100 and divide by GCD 4 to get 3:25, which is the same as about 1:8.33.
Can a percent over 100% become a ratio?
Not with the part-to-rest meaning, because the rest would be negative: 150% would give 150 : -50, which is meaningless. This calculator accepts percents from 0 to 100, which covers every real share-of-a-whole conversion.
What are 0% and 100% as ratios?
0% converts to 0:1, meaning there is no part at all. 100% converts to the degenerate form 1:0, meaning everything is the part and nothing remains.
How do you simplify a ratio?
Divide both terms by their greatest common divisor (GCD), the largest integer that divides both. Example: 25:75 has GCD 25, so 25/25 : 75/25 = 1:3. This calculator uses exact integer GCD math, never floating-point division.
Does this calculator round the answers?
No. Conversions use exact fraction and integer GCD math, so results are exact for terminating decimals. For example 33.33% converts to exactly 3333:6667, and only genuinely repeating decimals (like 300/43 = 6.976744186047...) are shown with an ellipsis.
Where can I see more percent to ratio conversions?
The common percent table on this page lists every whole percent from 1 to 99 with its simplified ratio, for example 12.5% = 1:7 and 2.5% = 1:39.
Free tool by NRTechStudio