Math

Ratio Calculator

Simplify ratios, scale them to equivalent ratios, or solve a proportion for the missing value.

:
Reduces A:B to lowest terms

Formulas

Simplify

A÷GCD(A,B) : B÷GCD(A,B)

Reduce a ratio to lowest terms

Scale by factor k

A×k : B×k

Create an equivalent, larger or smaller ratio

Proportion

A×D = B×C

Cross-multiplication solves A:B = C:D

Ratio → percentage

A ÷ (A+B) × 100

Share of A within the whole (A+B)

Percentage → ratio

P:(100−P), simplified

Write percentage as parts out of 100

Ratios, Fractions & Percentages

Ratio vs Fraction

A ratio A:B compares two quantities directly. A fraction A/(A+B) expresses one part's share of the combined whole — that's why 1:4 equals 20%, not 25%.

Equivalent ratios

Multiplying or dividing both terms by the same non-zero number never changes the underlying relationship — 2:3, 4:6, and 8:12 are all equivalent.

Proportions (A:B = C:D) show up in recipe scaling, map reading, unit conversion, and mixing ratios.

Tips

Simplify: Enter any two whole or decimal numbers — the calculator finds the GCD and reduces automatically.

Scale: Use a scale factor to blow a ratio up or down, or enter a target value for A or B to solve the other side.

Proportion: Leave exactly one of A, B, C, D blank — the calculator solves it via cross-multiplication.

FAQ

Frequently asked questions.

How do you simplify a ratio?

To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For example, to simplify 20:80, find the GCD of 20 and 80, which is 20, then divide both sides: 20÷20 = 1 and 80÷20 = 4, giving a simplified ratio of 1:4. This works the same way as reducing a fraction to lowest terms — the simplified ratio represents the exact same proportional relationship using the smallest whole numbers possible.

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

A proportion is solved using cross-multiplication: A×D = B×C. If three of the four values are known, rearrange to isolate the missing one. For example, in 2:3 = 8:?, cross-multiply to get 2×? = 3×8, so ? = 24÷2 = 12. This means 2:3 = 8:12, which you can verify by simplifying 8:12 back down to 2:3 (dividing both by their GCD of 4).

How do you convert a ratio to a percentage?

To convert a ratio A:B to a percentage, first find the total (A+B), then divide A by the total and multiply by 100. For example, the ratio 1:4 has a total of 5 parts, so 1÷5 = 0.20, or 20%. Similarly, a ratio of 3:5 has a total of 8 parts, so 3÷8 = 0.375, or 37.5%. This tells you what share of the whole the first term represents.

How do you convert a percentage to a ratio?

To convert a percentage to a ratio, write it as a fraction out of 100 and simplify. For example, 70% becomes 70:100, which simplifies by dividing both sides by their GCD of 10 to give 7:10. The second number in the resulting ratio represents the remaining share — in this case 30% — so 70:30 simplified is 7:3 if you are comparing the percentage directly against its complement.

What is an equivalent ratio?

Equivalent ratios express the same relationship between two quantities using different numbers, created by multiplying or dividing both terms by the same non-zero value. For example, 2:3 is equivalent to 4:6, 6:9, and 8:12 because each pair reduces back to 2:3. Equivalent ratios are useful for scaling recipes, mixing ratios, or map scales up or down while keeping proportions identical.

What is the ratio of 1 to 4 as a fraction and percentage?

The ratio 1:4 means 1 part out of a total of 5 parts (1+4), which as a fraction is 1/5 and as a percentage is 20%. Note this is different from the fraction 1/4 (25%) — 1:4 as a ratio compares the first term to the second term directly, while 1 part of a 5-part whole is the percentage share. Both interpretations are common depending on context, so this calculator shows the part-to-whole percentage explicitly.

Last updated: August 17, 2026