Proportion Calculator
Solve a:b = c:d for any missing value and check cross-products in seconds — for recipes, ratios and maps.
Solves a : b = c : d. Leave exactly one box empty — the calculator finds its value.
Missing value (d)
16
d = 16
Cross-product check
2 / 4 = 8 / 16
Both ratios equal
In a proportion, cross-products are equal: a × d = b × c. For 2/4 = 8/d, the missing denominator is 16 because 2 × 16 = 4 × 8.
Last updated: January 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Use the proportion calculator whenever two ratios must stay equal — scaling recipes, map distances, currency conversions, speed and time problems, or school ratio questions. Indian cooks scale ingredients for guests, builders use proportions to mix concrete and mortar, and map users convert centimetres on a map to kilometres on the ground — all classic a : b = c : d problems. Students preparing for competitive exams solve dozens of proportion questions, and this tool both computes the missing term and demonstrates the cross-product check that appears in every solution. Because exactly one box is left empty, the same screen solves for any of the four terms, and the equality check makes the result self-verifying. Any proportional relationship reduces to three quick inputs and an instant answer.
How to Use This Calculator
- Step 1: Enter three of the four values in a : b = c : d.
- Step 2: Leave exactly one box empty — the one you want to find.
- Step 3: Read the missing value and the cross-product verification.
- Step 4: Check that a × d equals b × c to confirm the proportion holds.
Worked Example
A recipe for 2 people uses 4 eggs, and a cook in Kochi needs the eggs for 8 people. Entering 2 : 4 = 8 : (blank) returns 16 — the missing term, since 2 × 16 = 4 × 8. A car covering 5 km in 2 minutes covers 20 km in 8 minutes: 5 : 2 = (blank) : 8 gives 20. Reversing the logic, if 3 workers make 9 items and 12 are needed, the missing workers term works out to 4.
Tips and Common Mistakes
- •Tip 1: Cross-products are equal in any proportion — a × d = b × c is the built-in verification.
- •Tip 2: Keep the same order of quantities in both ratios, or the proportion inverts and the answer flips.
- •Tip 3: Zero is allowed only as the missing value; a zero in a known term would make the ratio meaningless.
- ✗Mistake 1: Leaving more than one box empty — the calculator needs exactly three known values to solve.
- ✗Mistake 2: Mixing units across the ratio, like metres in one pair and kilograms in the other.
Sources and References
Official sources are linked so you can confirm the current rate yourself. Check the linked page for the latest notification before relying on these figures.
Frequently Asked Questions
What is a proportion?
A proportion states that two ratios are equal: a : b = c : d. If one of the four values is unknown, cross-multiplication a × d = b × c finds it. The calculator solves any missing value automatically.
How do I use the proportion calculator for recipes?
If a recipe uses 2 cups of flour with 3 cups of water, and you want 6 cups of water, enter a = 2, b = 3, c = empty, d = 6. The missing flour is 2 × 6 ÷ 3 = 4 cups — the calculator returns 4.
How are proportions used in everyday Indian life?
They appear in grocery scaling, map distances, mixing paints or fertilizers, and in school word problems — if 5 notebooks cost ₹75, how much do 8 cost? Setting up the proportion 5/75 = 8/x solves it.
What is cross-multiplication?
In a : b = c : d, multiply the outer terms and the inner terms: a × d = b × c. Then divide by the known number next to the unknown. The calculator shows this logic in the cross-product check card.
What happens if I leave more than one box empty?
The calculator needs exactly one missing value — with more blanks the proportion is underdetermined and it shows a hint asking you to fill in three values.
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