How do I solve a proportion?

Cross-multiply. For 3:4 = 15:x, 3x = 4 × 15, so x = 20.

How do I divide an amount in a ratio?

Add the parts, divide the total by that sum, then multiply by each part. 1,200 in 2:3:5 → 120 per share → 240, 360, 600.

Can a ratio have decimals?

Yes, but it is usually written in whole numbers. 1.5:2.25 equals 2:3.

Is a ratio the same as a fraction?

Related but different. 2:3 compares two parts; as fractions of the whole they are 2/5 and 3/5.

Can I use more than two parts?

Yes — the split mode accepts up to 10 parts, such as 1:2:3.

Math · Free tool

Ratio Calculator

Simplify ratios, solve proportions (a:b = c:x) and split a total in any ratio.

A ratio compares quantities: 2:3 means for every 2 of one thing there are 3 of another. Ratios turn up in recipes, screen sizes, map scales, mixing concrete or paint, and splitting money or profit fairly. Three questions cover almost every ratio problem, and this calculator has a mode for each.

Simplify reduces a ratio to its smallest whole-number form — 1920:1080 becomes 16:9 — by dividing both terms by their greatest common factor. Decimal ratios are scaled up first, so 1.5:2.25 becomes 2:3. Solve finds the missing term in a proportion a:b = c:x by cross-multiplication. Split divides a total in a given ratio, such as sharing 1,200 in the ratio 2:3:5.

Every mode shows the working so you can check it or copy it into homework.

By DailyCalc Editorial Team · Updated 2026-10-03 · 5-min read · 3 sources cited

● Ratio calculator

Math →

Ratio formulas

Simplify: a:b = (a ÷ g):(b ÷ g), g = GCF(a, b); Solve: x = b × c ÷ a; Split: shareᵢ = total × partᵢ ÷ Σparts

Simplifying divides both terms by their greatest common factor. Solving a proportion uses the fact that a/b = c/x means a × x = b × c. Splitting adds the parts to find how many equal shares there are, then gives each part its number of shares.

a, b: The two terms of the ratio a:b.
c, x: The known and unknown terms of the second ratio in a proportion.
g: Greatest common factor of a and b.

Worked examples: all three modes

One example of each kind of ratio question:

Simplify 1920:1080 — GCF is 120, so 1920 ÷ 120 : 1080 ÷ 120 = 16:9 (the widescreen ratio).
Simplify 1.5:2.25 — scale by 100 to 150:225, GCF 75, giving 2:3.
Solve 3:4 = 15:x — x = 4 × 15 ÷ 3 = 20.
Split 1,200 in 2:3:5 — 2 + 3 + 5 = 10 shares of 120 each, so 240, 360 and 600.
Check: 240 + 360 + 600 = 1,200 ✓ and 240:360:600 simplifies back to 2:3:5 ✓.

Result: 1920:1080 = 16:9 · 3:4 = 15:20 · 1,200 in 2:3:5 = 240 / 360 / 600.

How to use this ratio calculator

Choose the mode that matches your question.

Step 1: Simplify a:b

Enter both terms; decimals are fine. The result is in lowest whole-number terms, with the fraction and decimal forms.

Step 2: Solve a:b = c:x

Enter a, b and c to find the missing fourth term.

Step 3: Split a total

Enter the total and the ratio with colons, for example 2:3:5. Up to 10 parts.

Everyday ratio problems

Where people use each mode:

Scaling recipes

A recipe needs 250 g flour for 2 eggs; with 8 eggs, solve 2:250 = 8:x → 1,000 g.

Sharing money

Split profit between partners who invested in the ratio 2:3:5.

Screens and images

Simplify pixel dimensions to an aspect ratio before resizing.

Mixing

Concrete at 1:2:3 (cement:sand:gravel) — split the total volume you need.

Maps and models

On a 1:25,000 map, 4 cm represents 1 km; solve for any distance.

Pro tips

Keep ratio work clean:

Convert both terms to the same unit before comparing — 50 cm : 2 m is 1:4, not 25:1.
Order matters: 2:3 boys to girls is not 3:2.
To turn a ratio into fractions of the whole, divide each part by the sum: 2:3 means 2/5 and 3/5.
When splitting money, check the shares add back to the total after rounding.

Common mistakes

Errors that come up often:

Mixing units

Comparing 500 g to 2 kg as 500:2 instead of 500:2000 (1:4).

Dividing by the wrong total

Splitting 1,200 in 2:3 gives 480 and 720 — dividing by 2 and 3 separately gives nonsense.

Swapping terms in a proportion

a:b = c:x is not the same as a:b = x:c. Keep matching quantities in matching positions.

Stopping before lowest terms

1920:1080 → 192:108 is simpler but not simplest; keep going to 16:9.

Sources & references

The formula, thresholds and guidance on this page were checked against these primary sources. Written and reviewed by DailyCalc Editorial Team; last updated 2026-10-03. Spotted an error? Tell us.

FAQs