Ratio Calculator

Simplify ratios, solve proportions (a:b = c:?), scale ratios, and compare multiple ratios.

Mode

Reduce a ratio A : B to its simplest form.

Simplified Ratio

3 : 5

GCD = 5

Original ratio	15 : 25
Simplified	3 : 5
As decimal	1 : 1.666667
A as fraction of total	15/40 (37.50%)
B as fraction of total	25/40 (62.50%)

Results

Property	Formula
Simplify A:B	divide by GCD(A, B)
Proportion	A:B = C:D → D = BC/A
Part of total	A/(A+B) × 100%
As decimal	A ÷ B
Equivalent	A:B = kA:kB (any k)

Common Ratios

Ratio	Simplified	Decimal	Use
16:9	16:9	1.778	Widescreen
4:3	4:3	1.333	Standard screen
1:1	1:1	1.000	Square
3:2	3:2	1.500	Camera sensor
2:1	2:1	2.000	Panoramic
1:1.618	1:φ	0.618	Golden ratio
1:2	1:2	0.500	Half

The step this calculator uses to reduce a ratio, dividing repeatedly and keeping the remainder until nothing is left, is described in Book VII of Euclid's Elements, written around 300 BC, and it still works unchanged. Everything on the page, from simplifying 15:25 to reading a 1:500 plan, rests on that remainder trick or on cross-multiplication. Four tabs cover simplifying, solving proportions, scaling and comparing ratios side by side.

Three small examples and the formulas behind them

Simplify 15:25 and the page returns 3:5 with GCD = 5. It also shows 15/40 = 37.5% and 25/40 = 62.5% as shares of the total, plus an As decimal row of 1 : 1.666667. In Proportion mode, 3 : 4 = 9 : ? returns 12. In Scale mode, a 1 : 500 scale with 7.5 measured on the plan returns 3750 real units.

Where those numbers come from. GCD(15, 25) by Euclid: 25 mod 15 = 10, 15 mod 10 = 5, 10 mod 5 = 0, so the GCD is 5, and dividing both sides by 5 gives 3:5. Share of total is A ÷ (A + B) × 100. The As decimal row is B ÷ A written as 1 : x, so it shows how much B there is per 1 of A. The reference table on the page words this as A ÷ B, which is the reverse. The proportion D = (B × C) ÷ A comes from cross-multiplying A × D = B × C, here (4 × 9) ÷ 3 = 12. The scale answer is measured value × (real ÷ map) = 7.5 × (500 ÷ 1) = 3750.

Two behaviours to know. Simplify rounds A and B to whole numbers before reducing, so 1.5 : 2.5 is treated as 2 : 3. Scale decimals up first, for example 15 : 25. And a blank or zero in either Simplify box returns no result.

How to Use This Calculator

On Simplify, type A and B. Read the reduced ratio, the GCD and the percentage shares.
On Proportion, fill A, B and C for A : B = C : ?. The D box fills itself and the line beneath it shows the full equation.
On Scale, enter the map-side and real-side numbers of the scale (for 1:500, enter 1 and 500), then the measurement taken on the map or model.
On Compare, enter up to three A and B pairs. The table lists each in simplified form with its decimal value and A as a percentage of the total.
Read the reference table for common screen and camera ratios when you need a quick comparison.

Frequently Asked Questions

Do the units have to match on a scale?

The answer comes out in the unit you measured in. 7.5 cm on a 1:500 plan is 3750 cm, which is 37.5 m. Convert afterwards, because the page does not know the unit.

Why did 1.5:2.5 simplify to 2:3?

Simplify rounds each side to a whole number first, using standard rounding, so 1.5 becomes 2 and 2.5 becomes 3. Multiply both sides by 10 and enter 15 and 25 to get the true 3:5.

How do I split 800 in the ratio 3:5?

Enter 3 and 5 on Simplify. A is 37.5% of the total and B is 62.5%, so the shares are 800 × 0.375 = 300 and 800 × 0.625 = 500.

Does Compare recognise equal ratios?

Yes. Entering 2:3, 4:6 and 6:9 shows 2:3 in all three simplified cells, each with decimal 0.666667 and A at 40%. Keep to whole numbers for the cleanest output.

How do I find the aspect ratio of a 1920 × 1080 screen?

Enter 1920 and 1080 on Simplify. The GCD is 120, so the ratio reduces to 16:9, with an As decimal row of 1 : 0.5625.