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Proportion Calculator

Solve direct and inverse proportions instantly. Find missing values in ratios using cross multiplication, with step-by-step solutions. Free math tool for students and professionals.

Last revised 29 August 2026

By Team GlobalCalqulate · About our editorial standards

Proportion Setup

Proportion Type

Value A

Value B

Value C

Value D (leave blank to solve)

Solve For

Missing Value

2:4 = 6:12

Methodology

Formula:: Direct proportion
Content last updated:: August 2026
Scheduled re-verification:: August 2027

Calculation type: Exact calculation.

Formula & methodology

Formula used

Direct proportion

a ÷ b = c ÷ d   (equivalently a × d = b × c)

Two ratios are equal. Cross-multiplying gives the missing term — for example d = (b × c) ÷ a.

Inverse proportion

a × b = c × d

As one quantity rises the other falls, keeping the product constant. Twice the workers, half the time.

Variable definitions

Symbol	Meaning	Unit
a, b	First pair. the two terms of the known ratio	number
c, d	Second pair. the two terms of the second ratio, one of which is being solved for	number

Step-by-step calculation

1. Choose direct or inverse
Direct if the quantities rise together; inverse if one rises as the other falls.
2. Enter the three known terms and mark the fourth as unknown
The term being solved for is left out of the calculation.

Limitations

A proportion cannot be solved when the term that would become the denominator is zero — the calculator reports this rather than returning a value.
Assumes the relationship really is proportional across the whole range. Many real-world relationships are only approximately linear over a limited span.

This page is educational. It applies the formula described above to the figures you enter and shows the arithmetic behind the result. The output is only as good as the inputs and the assumptions listed here, and it is general information rather than advice about your particular situation.

Help & FAQs

Frequently Asked Questions

Clear answers to common questions to help you use this calculator confidently.

How to solve proportions?

Tap to view the answer

Use cross multiplication: multiply the means and extremes, then solve for the unknown.

What is direct proportion?

Tap to view the answer

Direct proportion means two quantities increase or decrease together at the same rate.

What is inverse proportion?

Tap to view the answer

Inverse proportion means one quantity increases as the other decreases.

How do I simplify a ratio?

Tap to view the answer

Divide both numbers by their greatest common factor (GCF).

Can I solve for any variable?

Tap to view the answer

Yes. Select which variable (A, B, C, or D) to solve for.

Need more help? Contact support or email globalcalqulate@gmail.com

We typically reply within 24–48 hours.

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How to Use This Calculator

Choose Proportion Type

Direct proportion (a:b = c:d) means as one value increases, the other increases proportionally. Inverse proportion means as one increases, the other decreases.

Enter Three Known Values

Fill in three of the four values (A, B, C, D) and leave the unknown blank. The calculator solves for the missing value.

Select Which Variable to Solve For

Choose which position (A, B, C, or D) contains your unknown. The calculator rearranges the formula automatically.

Review the Solution

See the missing value, the full proportion, and the simplified ratio. Direct proportions use cross-multiplication (a×d = b×c).

Understanding Your Results

Direct Proportion
Two quantities increase or decrease together: a/b = c/d. Example: if 2 apples cost $4, then 6 apples cost $12.
Inverse Proportion
One quantity increases as the other decreases: a×b = c×d. Example: doubling speed halves travel time.
Cross Multiplication
The key method: multiply extremes (a×d) and means (b×c), set equal, then solve for the unknown.

Key Tips

✓
Direct proportion: more of A means more of B (price, distance, ingredients).
✓
Inverse proportion: more of A means less of B (speed vs time, workers vs days).
✓
Always verify your answer by plugging it back into the original proportion.
✓
Simplified ratios help you see the constant relationship between the values.

Understanding Proportions

What Is a Proportion?

A proportion states that two ratios are equal: a:b = c:d. This means the relationship between a and b is the same as the relationship between c and d. Proportions are used everywhere: scaling recipes, converting currencies, calculating percentages, and solving for unknown quantities in science and engineering. The calculator solves proportions using cross multiplication, which works because equivalent fractions have equal cross products (a×d = b×c).

Direct vs Inverse Proportion — How to Tell Which One to Use

In direct proportion, the ratio a/b equals c/d — as one variable grows, the other grows at the same rate. Use direct proportion when the relationship is 'more → more' (more hours worked = more money earned, more ingredients = more servings). In inverse proportion, the product a×b equals c×d — as one grows, the other shrinks. Use inverse when the relationship is 'more → less' (more workers = fewer days to complete a job, higher speed = less travel time). If unsure, think about whether doubling one value should double or halve the other.

Cross Multiplication — The Engine Behind Proportion Solving

For a direct proportion a:b = c:d, cross multiplication gives a×d = b×c. Then solve for the unknown by dividing both sides by the coefficient. For example, 3:x = 9:15 → 3×15 = 9x → 45 = 9x → x = 5. For inverse proportion a:b = d:c, the cross multiplication becomes a×c = b×d. The calculator handles both cases — just select the type and enter your known values.

Real-World Applications

Proportions are everywhere: scaling a recipe (2 cups flour for 12 cookies → how much for 30 cookies?), currency conversion (1 USD = 0.92 EUR → how many EUR for 150 USD?), dosage calculations in medicine, map scale calculations, and unit conversions. The calculator shows results as a simplified ratio, a decimal, and a percentage — giving you multiple representations of the same proportional relationship.

Formula & methodology

Formula used

Direct proportion

a ÷ b = c ÷ d   (equivalently a × d = b × c)

Two ratios are equal. Cross-multiplying gives the missing term — for example d = (b × c) ÷ a.

Inverse proportion

a × b = c × d

As one quantity rises the other falls, keeping the product constant. Twice the workers, half the time.

Variable definitions

Symbol	Meaning	Unit
a, b	First pair. the two terms of the known ratio	number
c, d	Second pair. the two terms of the second ratio, one of which is being solved for	number

Step-by-step calculation

1. Choose direct or inverse
Direct if the quantities rise together; inverse if one rises as the other falls.
2. Enter the three known terms and mark the fourth as unknown
The term being solved for is left out of the calculation.

Limitations

A proportion cannot be solved when the term that would become the denominator is zero — the calculator reports this rather than returning a value.
Assumes the relationship really is proportional across the whole range. Many real-world relationships are only approximately linear over a limited span.

Calculator inputs

Proportion Setup

Your results

Methodology

Formula & methodology

Formula used

Direct proportion

Inverse proportion

Variable definitions

Step-by-step calculation

Limitations

How to solve proportions?

What is direct proportion?

What is inverse proportion?

How do I simplify a ratio?

Can I solve for any variable?

Related calculators

More everyday calculators

Calculator inputs

Proportion Setup

Your results

Methodology

How to Use This Calculator

Example: Solve 2:4 = 6:x

Understanding Your Results

Key Tips

Understanding Proportions

What Is a Proportion?

Direct vs Inverse Proportion — How to Tell Which One to Use

Cross Multiplication — The Engine Behind Proportion Solving

Real-World Applications

Formula & methodology

Formula used

Direct proportion

Inverse proportion

Variable definitions

Step-by-step calculation

Limitations

How to Use This Calculator

Example: Solve 2:4 = 6:x

Understanding Your Results

Key Tips

Understanding Proportions

What Is a Proportion?

Direct vs Inverse Proportion — How to Tell Which One to Use

Cross Multiplication — The Engine Behind Proportion Solving

Real-World Applications