Example 1
- a = 12
- b = 8
3 : 2
Divide both by GCD = 4.
Ratio of two numbers calculator
Type two integers. The calculator divides them by the GCD and shows the reduced ratio. 12 : 8 has GCD = 4, so 3 : 2. 45 : 15 has GCD = 15, so 3 : 1.
This calculator works with integers only. Decimals are not supported - enter 12 and 8, not 12.5.
Result
Enter two whole numbers to simplify the ratio.
How does it work?
A ratio a : b compares two quantities. To reduce it, divide both numbers by their GCD (greatest common divisor). 12 : 8, GCD is 4, so 12÷4 = 3 and 8÷4 = 2. The reduced ratio is 3 : 2. 45 : 15 gives 3 : 1. 7 : 3 stays 7 : 3, because GCD = 1.
The calculator works on integers. A fraction 12.5 does not run. 100 : 25 reduces by 25 to 4 : 1. 84 : 36 has GCD = 12, ratio 7 : 3.
Fields: First number and Second number. Type 12 and 8, click Calculate. A minus usually folds into absolute values when reducing. Zero in the second number does not build a 7:0 ratio.
GCD(12, 8) = 4 also lives on the GCD page. Splitting 100 in a ready 3 : 2 is on divide in a ratio (60 and 40). The rule of three builds a fourth number from three; it does not reduce a pair.
Without both integers, nothing computes. 12 and 8 still give 3 : 2 no matter the header.
144 : 96 has GCD = 48, ratio 3 : 2. 270 : 192 needs reducing by its GCD. Check 12 and 8 first.
Formula
For integers a and b (b ≠ 0):
a : b = (a ÷ GCD) : (b ÷ GCD)
How to use
- Type the first integer, for example 12.
- Type the second integer, for example 8.
- Click Calculate. 12 : 8 becomes 3 : 2. 45 : 15 becomes 3 : 1.
- A fraction 12.5 does not run. GCD = 1 leaves the ratio unreduced, like 7 : 3.
- Bare GCD(12, 8) = 4 lives on GCD. Splitting a whole in 3 : 2 lives on divide in a ratio.
GCD reduces 12 : 8 to 3 : 2
A ratio of two numbers is divided by the GCD. 12 : 8 has GCD = 4, so 3 : 2. 45 : 15 has GCD = 15, so 3 : 1.
- GCD
- The divisor used to reduce the pair. GCD(12, 8) = 4, hence 3 : 2. GCD(7, 3) = 1 leaves 7 : 3.
- 12 : 8
- The pair before reducing. After GCD = 4 it becomes 3 : 2. 144 : 96 reduces to the same 3 : 2.
Examples
Example 2
- a = 45
- b = 15
3 : 1
45 and 15 share the factor 15.
Example 3
- a = 7
- b = 3
7 : 3
GCD = 1 - no reduction needed.
Example 4
- a = 100
- b = 25
4 : 1
Large numbers reduce quickly with GCD = 25.
Example 5
- First number: 7
- Second number: 0
No ratio
Does 7:0 yield a ratio here? No. A zero in the second number does not build a ratio.
Related calculators
Frequently asked questions
What is the ratio 12 : 8?
The reduced ratio is 3 : 2. The GCD, greatest common divisor, is 4. 12÷4 = 3, 8÷4 = 2.
What is 45 : 15?
You get 3 : 1. The common divisor is 15. 45÷15 = 3, 15÷15 = 1. One part to three.
Does 7 : 3 need reducing?
No. GCD = 1, so the ratio stays 7 : 3. The pair is already in lowest terms.
What are 100 : 25 and 84 : 36?
100 : 25 reduces to 4 : 1, GCD = 25. 84 : 36 reduces to 7 : 3, GCD = 12.
Why does 12.5 fail?
Integers only. Decimal fractions are rejected. Type 25 : 10 as whole numbers and you get 5 : 2.
How is this different from GCD?
GCD(12, 8) = 4 is one number on the GCD page. Here 4 is used to shrink the pair to 3 : 2.
Where do I split 100 in 3 : 2?
On divide in a ratio. You get 60 and 40. Here you only reduce two numbers, you do not split a whole.
Does 7 : 0 run?
No. A zero in the second number does not make a ratio on this page. There is no divide by zero and no reduced pair.
What is 144 : 96?
You get 3 : 2. GCD = 48. The same reduced ratio as 12 : 8, only larger numbers at the start.
Does the rule of three reduce 12 : 8?
No. The rule of three hunts a fourth number from three known ones. Reducing a pair stays here.
Knowledge sources
The calculator computes the same formula as the definition below.
Page updated in 2026.