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Ratio Calculator

Solve ratios and proportions

Simplified Ratio

3:2

Mode

Simplify

Decimal

1.5000

Enter a ratio to simplify

:

Simplified Ratio

3 : 2

Decimal: 1.5000

Visual Ratio

A12
B8

Formulas Used

Simplify Ratio

Simplified = (a / GCD) : (b / GCD)

Simplify a ratio by dividing both parts by their Greatest Common Divisor.

Where:

a : b= The original ratio
GCD= Greatest Common Divisor of a and b

Solve Proportion

X = (b × c) / a

Solve for X in the proportion a/b = c/X using cross-multiplication.

Where:

a= First ratio numerator
b= First ratio denominator
c= Second ratio numerator
X= Unknown value to solve for

Example Calculations

1Simplify Ratio 12:8

Inputs

ModeSimplify
Ratio12 : 8

Result

Simplified Ratio3 : 2
Decimal1.5000

Find the GCD of 12 and 8, which is 4. Divide both parts: 12/4 = 3, 8/4 = 2. Simplified ratio is 3:2. Decimal = 12/8 = 1.5000.

2Solve Proportion: 2/5 = 10/X

Inputs

ModeSolve X
a2
b5
c10

Result

X25.00

Using cross-multiplication: X = (b × c) / a = (5 × 10) / 2 = 50 / 2 = 25.00.

Frequently Asked Questions

Q

What is a ratio and how do I write it?

A ratio compares two or more quantities. Write as 3:2, 3 to 2, or 3/2. Example: 6 boys to 4 girls = 6:4 = 3:2 simplified. Ratios can have any number of parts: 1:2:3 means "1 part to 2 parts to 3 parts."

  • Notation: 3:2, 3 to 2, or 3/2 (all equivalent)
  • Simplify like fractions: 6:4 = 3:2
  • Order matters: 3:2 ≠ 2:3
  • Can have multiple parts: 1:2:3
  • Total parts in 3:2 = 3+2 = 5 parts
RatioSimplifiedFractionPercentage of First
1:11:11/1 or 150% each
2:12:12/1 or 267% vs 33%
3:23:23/2 or 1.560% vs 40%
4:34:34/3 or 1.3357% vs 43%
16:916:916/9 or 1.78Widescreen TV
Q

How do I solve a proportion for an unknown value?

Cross-multiply and divide. If a:b = c:x, then x = (b×c)÷a. Example: 3:5 = 12:x. Cross-multiply: 3×x = 5×12. So 3x = 60, x = 20. Check: 3:5 = 12:20 ✓ (both simplify to 3:5).

  • Set up: a/b = c/x
  • Cross multiply: a×x = b×c
  • Solve for x: x = (b×c)/a
  • Always check: Simplify both ratios to verify
  • Works for any position of unknown
ProportionCross MultiplySolveAnswer
2:3 = 4:x2×x = 3×42x = 12x = 6
5:8 = x:245×24 = 8×x120 = 8xx = 15
x:4 = 6:8x×8 = 4×68x = 24x = 3
Q

How do I convert a ratio to a fraction or percentage?

For ratio a:b, the first quantity is a/(a+b) of the total. Example: 3:2 ratio means first is 3/5 = 60%, second is 2/5 = 40%. For fraction of first to second: 3:2 = 3/2 = 1.5.

  • Part to whole: a/(a+b) for first part
  • Ratio 3:2: First = 3/5 = 60%
  • Ratio 3:2: Second = 2/5 = 40%
  • Ratio to fraction: 3:2 = 3/2
  • Fraction to ratio: 3/4 = 3:4
RatioFirst Part %Second Part %As Fraction
1:150%50%1/1
2:166.7%33.3%2/1
3:175%25%3/1
3:260%40%3/2
4:180%20%4/1
Q

What are common real-world ratio applications?

Recipes (flour:sugar = 2:1), maps (scale 1:100000), mixing (paint 3:1:1), aspect ratios (16:9 TV), finance (debt-to-income 36:100), golden ratio (1:1.618), and probability (odds 3:1).

  • Recipes: Scale ingredients proportionally
  • Maps: Distance ratios (scale)
  • Screen: 16:9 (widescreen), 4:3 (old TV)
  • Mixing: Paint, concrete, cocktails
  • Finance: Debt-to-income, P/E ratio
ApplicationExample RatioMeaning
Recipe scaling2:1 flour:sugarDouble flour for sugar
Map scale1:100,0001cm = 1km
TV aspect ratio16:9Width to height
Photo aspect ratio4:3 or 3:2Standard photo sizes
Golden ratio1:1.618Aesthetically pleasing
Odds (betting)3:13 wins for every 1 loss
Q

How do I scale a ratio up or down?

Multiply or divide both parts by the same number. Example: 3:2 scaled up ×4 = 12:8. To scale 2:3 to have 15 in second part: 3→15 means ×5, so 2×5:3×5 = 10:15.

  • Scale up: Multiply both parts by same number
  • Scale down: Divide both parts (if divisible)
  • 3:2 × 4 = 12:8 (same ratio)
  • To get specific total: Find multiplier
  • Example: 2:3 total 100 → ×20 = 40:60
Original×2×5×10
1:22:45:1010:20
2:34:610:1520:30
3:46:815:2030:40
Q

How do I simplify a ratio?

Divide both parts by their greatest common divisor (GCD). Example: 12:8 → GCD is 4 → 12÷4:8÷4 = 3:2. For decimals, multiply to remove decimals first: 0.5:1.5 = 5:15 = 1:3.

  • Find GCD of both numbers
  • Divide both by GCD
  • 12:8 → ÷4 → 3:2
  • Decimals: Multiply by 10 or 100 first
  • 0.5:2 → 5:20 → 1:4
Original RatioGCDSimplified
4:841:2
12:1862:3
15:2553:5
100:250502:5

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Last Updated: Mar 11, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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