Ratio Calculator

Calculated using standard mathematical and industry formulas.

Free online Ratio Calculator calculator for academic, engineering, and statistical math.

How to use this calculator?

1. Select the mode: simplify a ratio, solve a proportion, or split a total.
2. For simplification: enter A and B — the calculator divides both by their GCF.
3. For proportion: enter three known values and set the unknown to 0.
4. For splitting: enter the total amount and a ratio like 2:3:5 to get each share.

Formula & calculation method

Ratio simplification and proportion solving

Simplified ratio = A/GCF : B/GCF · Proportion: A × D = B × C · Split: unit = Total / ΣParts, share_i = part_i × unit

GCF = greatest common factor. Use the GCF Calculator to find it step by step.

Step-by-step calculation example

12:16 → GCF = 4 → 3:4. Proportion: 3/4 = 6/? → D = (4×6)/3 = 8. Split 500 in 2:3:5 → 100:150:250.

Key insights to remember

• A ratio a:b is simplified by dividing both terms by their greatest common factor (GCF).
• Proportions A/B = C/D are solved by cross-multiplication: A × D = B × C.
• Dividing 500 in ratio 2:3:5 gives 10 equal parts, worth 50 each: 100, 150, 250.
• Ratios are used in map scales, recipe scaling, finance (debt-to-equity), and image aspect ratios.

How to interpret your results?

Simplified ratio

Dividing A and B by their GCF gives the simplest form. 12:16 → GCF = 4 → 3:4.

Cross-multiplication

If A/B = C/D then A × D = B × C. This finds the missing term when three values are known.

Frequently asked questions

How does the Ratio Calculator calculator work?

It uses standard algebraic, geometric, or statistical theorems to return exact values.

How accurate are the results?

All calculations use double-precision floating-point arithmetic for exact accuracy.

Can I copy the step-by-step work?

Yes, step-by-step solutions are formatted clearly for homework or documentation.

How are undefined operations handled?

The calculator flags mathematical errors such as division by zero or negative square roots.

Is this tool suitable for students and engineers?

Yes, it is designed for students, teachers, engineers, and scientists.

Does it support negative numbers and decimals?

Yes, all real numbers (positive, negative, fractions, and decimals) are supported.

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