Proportion Calculator
Solve a missing value in A:B = C:D, check equivalent ratios, and see the cross-multiplication step.
Answer
D = 10
Completed Proportion
3:6 = 5:10
Cross-Multiplication
Decimal (A:B)
0.5000
Decimal (C:D)
0.5000
Scale Factor
Right side = left side × 1.6667
Steps
Cross multiply: 3 × 10 = 6 × 5
Isolate unknown: D = (6 × 5) / 3
Check: 30.0000 = 30.0000
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What this does
Enter three values in the proportion A:B = C:D. The calculator finds the missing fourth value, checks the completed proportion, and shows the cross-multiplication step.
Who it is for
Students solving proportion homework, teachers checking work, and anyone scaling recipes, maps, drawings, or dimensions.
How it works
The cross-product rule A × D = B × C is used to isolate the unknown. Enter any three values and the fourth is computed immediately.
Limitations
One unknown at a time. Two or more unknowns cannot produce a single numeric answer. Values cannot create a zero denominator.
Key calculations
- Cross-Product Rule
- For any true proportion A:B = C:D, the cross products are equal: A × D = B × C.
- Solve Missing A
- A = (B × C) / D
- Solve Missing B
- B = (A × D) / C
- Solve Missing C
- C = (A × D) / B
- Solve Missing D
- D = (B × C) / A
Reference ranges
- Direct Proportion
- When one ratio equals another. If 3:4 = 6:8, then 3/4 = 6/8 = 0.75. All four values form a true proportion.
- Scaling Up
- Multiply both terms of the left ratio by the same factor to get the right ratio. Example: 3:4 scaled by 2 gives 6:8.
- Scaling Down
- Divide both terms of the left ratio by the same factor. Example: 6:8 scaled by 2 gives 3:4.
How to use it
- 1.Enter three known valuesFill any three of the four fields A, B, C, and D. Leave exactly one field blank or type a single letter like x.
- 2.Read the answerThe missing value is computed instantly. The completed proportion, cross-multiplication steps, decimal equivalents, and scale factor appear below the inputs.
- 3.Check equivalenceFill all four fields to check whether the ratios are truly proportional. The calculator compares cross products and reports whether they match.
Use cross-multiplication: for A:B = C:D, multiply A × D and B × C. These products must be equal. If one value is unknown, rearrange to isolate it.
Two ratios are equivalent when cross-products are equal. For example, 3:4 and 6:8 are equivalent because 3 × 8 = 4 × 6 = 24.
Yes. Type x, y, or any single letter in one field. The calculator treats it as the unknown and solves for it.
With two or more unknowns, a proportion has infinitely many solutions. The calculator shows an underdetermined state instead.
Yes. The calculator parses simple fraction strings like 3/4, 1/2, or -2/3.
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