Ratio & Proportion Calculator

How to Use the Ratio Calculator

Choose the calculation you need. Simplify reduces a ratio to lowest whole-number terms. Equivalent finds a matching value in a new ratio. Proportion solves one missing value in A/B = C/D. Scale multiplies or divides both parts by the same factor.

Enter positive values in the required fields. Decimal values with up to six decimal places are supported.

The result updates automatically as you change the inputs.

What Is a Ratio?

A ratio compares two quantities in a particular order. The ratio of A to B can be written as A:B, A to B, or A/B.

For example, 2:3 means that for every 2 units of the first quantity there are 3 corresponding units of the second quantity.

Order matters. The ratio 2:3 is not the same comparison as 3:2. Their quotients are 2/3 and 3/2 respectively.

How to Simplify a Ratio

A ratio is in lowest terms when its two whole-number parts have no common factor greater than 1.

To simplify a whole-number ratio, find the greatest common divisor (GCD) of both values and divide each value by it.

For example, the GCD of 20 and 30 is 10. Dividing both values by 10 changes 20:30 into 2:3 without changing the relationship.

Simplifying Ratios With Decimals

Ratios containing decimals can also be reduced to whole-number terms. A convenient method is to multiply both values by the same power of 10 until the decimals are removed, then simplify the resulting whole-number ratio.

For example, 1.5:2.5 can be multiplied by 10 to give 15:25. Dividing both parts by 5 gives the simplified ratio 3:5.

This calculator supports up to six decimal places. Internally, it converts the entered decimals to equivalent scaled whole numbers before finding their greatest common divisor.

What Is an Equivalent Ratio?

Equivalent ratios express the same proportional relationship using different numbers. For example, 2:3, 4:6, and 10:15 are equivalent.

You can create an equivalent ratio by multiplying or dividing both parts by the same nonzero factor.

If 2:3 is changed so that the first value becomes 10, the scale factor is 5. Multiplying the second value by the same factor gives 15, so the equivalent ratio is 10:15.

How to Find a Missing Value in an Equivalent Ratio

If one part of a new equivalent ratio is known, first determine how the corresponding part of the original ratio changed.

For example, starting with 4:7, suppose the first value in the new ratio is 12. Because 4 was multiplied by 3, multiply 7 by 3 as well. The missing value is 21, giving 12:21.

The calculator can solve from either side of the ratio, so the known value can correspond to the first or second part.

What Is a Proportion?

A proportion is an equation stating that two ratios are equal. A common form is A/B = C/D.

For example, 2/3 = 10/15 is a valid proportion because both ratios describe the same relationship.

When three of the four values are known, the remaining value can be solved algebraically.

How to Solve a Proportion

Enter three values in A/B = C/D and leave exactly one field blank. The calculator determines which value is missing and solves for it.

For example, 2/3 = 10/x can be solved by cross multiplication. This gives 2x = 30, so x = 15.

Keep corresponding quantities in the same position on both sides. If the first ratio is students per teacher, for example, the second ratio should also place students and teachers in the same order.

How Cross Multiplication Works

For the proportion A/B = C/D, multiplying both sides by B × D gives the equivalent relationship A × D = B × C.

That equation can then be rearranged to solve whichever one of A, B, C, or D is unknown.

Cross multiplication applies when two ratios are set equal as a proportion. It should not be treated as a general shortcut for every equation that happens to contain fractions.

How to Scale a Ratio

Scaling a ratio changes the size of both values while preserving their relationship.

Multiplying 3:4 by 5 gives 15:20. Dividing both values of 15:20 by 5 returns 3:4.

Both parts must use the same scale factor. Multiplying only one side changes the ratio instead of creating an equivalent one.

Ratio Order Matters

A ratio describes the first quantity relative to the second, so reversing the values changes its meaning.

If a group contains 2 red objects and 3 blue objects, the red-to-blue ratio is 2:3. The blue-to-red ratio is 3:2.

This also matters when solving proportions. Corresponding quantities should occupy matching positions in both ratios.

Part-to-Part and Part-to-Whole Ratios

A ratio can compare one part with another part or compare one part with the complete total.

Suppose a group contains 2 red objects and 3 blue objects. The red-to-blue ratio is 2:3, while the red-to-total ratio is 2:5 because there are 5 objects altogether.

These describe different comparisons even though they come from the same group.

Ratio vs Fraction

Ratios and fractions often use similar notation, but their interpretation depends on context.

A ratio can compare part to part, part to whole, or one quantity with another. A fraction commonly represents a part of a whole or a numerical quotient.

For example, a red-to-blue ratio of 2:3 does not mean that red objects make up 2/3 of the complete group. With 2 red and 3 blue objects, the red share of the total is 2/5.

Ratio vs Percentage

A percentage expresses a quantity relative to 100, while a ratio directly compares two quantities.

For the ratio 1:4, the first quantity is 25% of the second quantity because 1 ÷ 4 = 0.25.

That is different from asking what percentage the first part represents of the combined total. If the parts are 1 and 4, the total is 5, so the first part represents 1/5 = 20% of the total.

Ratios and Rates

Ratios compare quantities. When the comparison involves quantities measured in different units, it is often described as a rate.

For example, 150 kilometres in 3 hours can be expressed as 150 km : 3 h. Dividing both values by 3 gives the unit rate 50 kilometres per hour.

This calculator handles the numerical ratio itself. It does not attach or convert measurement units.

Common Ratio and Proportion Mistakes

Reversing the order: 2:5 and 5:2 represent different comparisons.

Scaling only one part: Both values must be multiplied or divided by the same factor to preserve the ratio.

Using inconsistent positions in a proportion: Corresponding quantities should appear in the same numerator or denominator position.

Confusing part-to-part with part-to-whole: A 2:3 part-to-part ratio contains 5 total parts, not 3.

Cross multiplying outside a proportion: The shortcut A × D = B × C applies to two ratios set equal as A/B = C/D.

How This Ratio Calculator Works

In Simplify mode, decimal inputs are converted to scaled integers and reduced using their greatest common divisor. This allows values such as 1.5:2.5 to simplify exactly to 3:5 within the calculator's supported precision.

Equivalent mode preserves the relationship A/B by solving for the corresponding value after one side is changed.

Proportion mode identifies the single blank value in A/B = C/D and rearranges the cross-product equation A × D = B × C to solve it.

Scale mode multiplies or divides both ratio values by the same positive factor.

Ratio and Proportion Formulas

Equivalent ratios have the same quotient. A proportion sets two ratios equal, allowing a missing value to be found algebraically.

$A$

First value in the first ratio

$B$

Second value in the first ratio

$C$

First value in the second ratio

$D$

Second value in the second ratio

$k$

Positive scale factor

Examples

Frequently Asked Questions

References

• OpenStax Contemporary Mathematics - Ratios and Proportions
• OpenStax Prealgebra 2e - Solve Proportions and Their Applications