⚖️ Knowledge · Maths

How to Calculate
Ratio

Simplify ratios, scale quantities, and divide amounts in any ratio — with step-by-step explanations and a free calculator.

What is a Ratio?

Ratio a : b = a ÷ GCD : b ÷ GCD

A ratio compares two or more quantities. To simplify, divide both values by their Greatest Common Divisor (GCD).

💡 Example: Ratio 12:8 → GCD is 4 → Simplified: 3:2. As a fraction: 3/2. As a decimal: 1.5. As percentage: 60% to 40%.

Ratio Calculator

:
Simplified Ratio
3 : 2
GCD = 4
As Fraction
3/2
As Decimal
1.5
A as %
60%
B as %
40%
:
How to Split 100
Part A (3 shares)60
Part B (2 shares)40
:
Scaled Ratio
15 : 10
3×5 : 2×5

Step-by-Step: Simplify a Ratio

1

Write the ratio

Example: 18:12 (18 parts to 12 parts)

2

Find the GCD

Greatest Common Divisor of 18 and 12. Factors of 18: 1,2,3,6,9,18. Factors of 12: 1,2,3,4,6,12. GCD = 6.

3

Divide both parts by the GCD

18 ÷ 6 = 3. 12 ÷ 6 = 2. Simplified ratio: 3:2

Worked Examples

Recipe Scale

Recipe for 4: flour 2:butter 1
Scale up for 12 people
Factor: 3
6 cups : 3 cups

Share Profit

Partners A:B = 3:2
Total profit: $5,000
A = 3/5 × 5000
A=$3,000, B=$2,000

Simplify 24:36

GCD(24,36) = 12
24÷12 : 36÷12
2 : 3

Map Scale

1:50,000 map
5cm on map =
5 × 50,000cm
2.5 km in reality

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📊
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Frequently Asked Questions

What is the difference between ratio and fraction? ▾
A ratio (3:2) compares two separate quantities. A fraction (3/5) represents part of a whole — where the denominator is the total. The ratio 3:2 means 3 out of every 5 total parts, which is 3/5 for the first part.
How do I find the ratio of two numbers? ▾
Write them as A:B, then simplify by dividing both by their GCD. Example: 30 and 45 → GCD is 15 → 30:45 simplifies to 2:3.
Can a ratio have decimals? ▾
Ratios can have decimals, but it's conventional to express them as whole numbers. If you have 1.5:1, multiply both by 2 to get 3:2.