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Ratio Calculator

Solve proportions and simplify ratios.

Simplify Ratio

Reduce a ratio to its simplest form.

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Ratio Proportion Solver

Solve for the missing value in A : B = C : D.

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Ratio Scaling Calculator

Enlarge or reduce a ratio by a given factor.

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Calculation Breakdown:

Enter values to compute result.

About this topic

Simplify Ratio Scale down a ratio to its smallest whole numbers.

A ratio compares two or more quantities and shows how much of one there is in relation to another. Simplifying a ratio works like simplifying a fraction: divide every term by the same greatest common divisor. For example, a mixture containing 12 cups of water and 18 cups of juice has a ratio of 12:18, which simplifies to 2:3. The relationship stays the same even though the numbers become smaller.

Key formulas & rules

  • •Uses Greatest Common Divisor
  • •Both terms must be integers
  • •Maintains the exact proportion
  • •Result is the simplest form
  • •Equivalent to simplifying a fraction

Examples

Input Output Note
12:18 2:3 Divide by 6
50:100 1:2 Divide by 50
7:9 7:9 Already simplified
1000:500 2:1 Divide by 500

Real-world uses

Recipe scaling Map scales Aspect ratios
Proportion Solver Find the missing value in a proportion (A:B = C:D).

A proportion states that two ratios are equivalent. If three values are known, cross-multiplication can be used to calculate the missing fourth value. For example, if 2 items cost $3, then 4 items at the same rate cost $6 because 2:3 = 4:6. Proportions are useful for scaling recipes, reading maps, comparing prices, and converting measurements, provided the relationship is directly proportional.

Key formulas & rules

  • •Cross-multiplication: A × D = B × C
  • •Requires exactly 3 known values
  • •Works for any units
  • •Solves for A, B, C, or D
  • •Assumes a direct proportion

Examples

Input Output Note
2:3 = 4:? D = 6 Cross multiply
2:3 = ?:6 C = 4 Solves for C
1:2 = 5:? D = 10 Simple scaling
? : 4 = 3 : 6 A = 2 Solves for A

Real-world uses

Adjusting recipes Scale drawings Currency exchange
Scale Ratio Enlarge or shrink a ratio by a specific factor.

Scaling a ratio means multiplying or dividing every term by the same factor. Because both terms change equally, the relationship between them remains unchanged. For example, a recipe that uses 1 cup of rice for every 2 cups of water has a ratio of 1:2; multiplying both terms by 3 gives 3:6 for a larger batch. Scaling by 1/2 would reduce 4:8 to 2:4 without changing the proportion.

Key formulas & rules

  • •Multiplies both terms by factor
  • •Factor can be a fraction
  • •Preserves the proportion
  • •Useful for batch cooking
  • •Factor cannot be zero

Examples

Input Output Note
1:2 scaled by 3 3:6 Enlarging
4:8 scaled by 1/2 2:4 Shrinking
3:5 scaled by 2 6:10 Doubling
10:20 scaled by 1/10 1:2 Reducing

Real-world uses

Batch cooking Model building Blueprint reading

Modes & formulas

1

Simplify Ratio

• Scales down a ratio to its smallest whole numbers. • Enter the two terms of the ratio. • The calculator finds the Greatest Common Divisor (GCD) and divides both terms.
A : B ÷ GCD = (A/GCD) : (B/GCD)

Just like simplifying a fraction, a simplified ratio maintains the same exact relationship between the two numbers but uses smaller, easier-to-read terms.

2

Proportion Solver

• Finds the missing value in a proportion (A : B = C : D). • Enter any three of the four values. • The calculator uses cross-multiplication to solve for the unknown variable.
A × D = B × C

Multiply the outer terms (A and D) and the inner terms (B and C). If you know A, B, and C, you can find D by (B × C) / A.

3

Scale Ratio

• Enlarges or shrinks a ratio by a specific factor. • Enter the ratio and the scale factor. • The calculator multiplies or divides both terms by the factor.
A : B × Factor = (A×F) : (B×F)

Scaling up maintains the exact same proportions. For example, a recipe ratio of 1:2 scaled by 3 becomes 3:6.

How to use it

Choose the tab for Simplifying, Solving Proportions, or Scaling. Enter your known values and the calculator will handle the cross-multiplication and GCD reductions instantly.

Frequently asked questions

What is a proportion?
An equation stating that two ratios are equal, like 1/2 = 2/4.
Can a ratio have decimals?
Yes, but it's usually clearer to scale both terms by a power of 10 to remove the decimals, then simplify.
What is a ratio?
A ratio compares two quantities and shows how many times one contains the other. 2:3 means for every 2 of the first item, there are 3 of the second.
How do I simplify a ratio?
Divide both terms by their greatest common divisor. For 12:18, the GCD is 6, so the ratio simplifies to 2:3.
Can ratios have decimals?
Yes, but they are usually clearer as whole numbers. Multiply both terms by a power of 10 to remove decimals, then simplify.
How do I solve a proportion?
Cross-multiply: A × D = B × C. If you know three of the four values, you can find the fourth.

Related calculators

Percentage Calculate percentages, increases, and decreases. Fraction Add, subtract, multiply, and divide fractions. Average Find mean, median, and average of a dataset. Exponent & Root Calculate powers and bases. Square Root & N-th Root Find square roots and radical values. Linear Equation Solve equations of the form ax + b = c.
Read the full Ratio guide — examples & 18 FAQs