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Proportion Calculator

Solve proportions like a/b = c/d. Choose which value is missing, enter the other three, and get the answer with clear cross‑multiplication steps. Great for scaling recipes, maps, resizing images, unit pricing, and schoolwork.

⚡Instant missing‑value solve
🧾Shows cross‑multiplication steps
✅Auto ratio check (a·d vs b·c)
📱Screenshot‑friendly & shareable

Enter your proportion

Pick the missing value, then fill the other three numbers. You can use whole numbers or decimals. The calculator solves a/b = c/d and shows the exact steps.

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Your result will appear here
Choose the missing value, enter the other three numbers, then tap “Solve Proportion”.
Steps will show cross-multiplication: a·d = b·c.
Quick check: the two ratios should match (within rounding). Higher bar = closer match.
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📘 Guide

Proportion Calculator: solve “A is to B as C is to D”

Use this free Proportion Calculator to solve equations like a/b = c/d. Pick which value is missing, enter the other three, and get the answer instantly—plus the exact algebra steps (cross-multiplication) so you can double-check.

🧠 What is a proportion?

A proportion is an equation that says two ratios are equal. If you write a/b = c/d, you’re saying “the ratio of a to b is the same as the ratio of c to d.” People use proportions constantly, even when they don’t call it that: scaling a recipe, resizing an image, reading a map, mixing paint, adjusting a medication dosage, or comparing prices and quantities.

The power of proportions is that they let you solve for an unknown using the values you already know. If three numbers are known, the fourth is determined (as long as you’re not dividing by zero).

Common proportion formats
  • a/b = c/d (ratio form)
  • a : b = c : d (colon form)
  • a is to b as c is to d (word form)
  • part/whole = part/whole (rates and shares)
➗ The core formula (cross-multiplication)

Starting with a/b = c/d, multiply both sides by b·d to clear denominators:

  • a/b = c/d
  • Multiply both sides by b·d
  • a·d = b·c (cross-multiplication)

From a·d = b·c, you can solve for any missing variable:

  • If d is missing: d = (b·c)/a
  • If a is missing: a = (b·c)/d
  • If b is missing: b = (a·d)/c
  • If c is missing: c = (a·d)/b
🧾 Real-life examples you can copy

Example 1: Recipe scaling

A recipe uses 3 cups of flour for 12 cookies. How much flour for 20 cookies? Set up the proportion (flour/cookies stays constant):

  • 3 / 12 = x / 20
  • Cross-multiply: 3·20 = 12·x
  • 60 = 12x
  • x = 60/12 = 5

Answer: 5 cups of flour for 20 cookies.

Example 2: Map scale

A map scale says 1 inch = 50 miles. If two cities are 3.4 inches apart on the map, what is the real distance?

  • 1 / 50 = 3.4 / x
  • Cross-multiply: 1·x = 50·3.4
  • x = 170

Answer: 170 miles.

Example 3: Unit price / bulk shopping

If 5 pounds of rice costs $8, how much do 12 pounds cost at the same rate?

  • 8 / 5 = x / 12
  • Cross-multiply: 8·12 = 5x
  • 96 = 5x
  • x = 19.2

Answer: $19.20.

Example 4: Photo resizing

You have an image that’s 1200 px wide and 800 px tall. You want it 900 px wide without stretching. What height should it be?

  • 1200 / 800 = 900 / x
  • Cross-multiply: 1200·x = 800·900
  • x = 600

Answer: 600 px.

🔍 How this calculator works

This calculator rewrites the proportion into a cross-multiplication equation a·d = b·c, then isolates the missing value by dividing both sides.

  • Shows the completed proportion with your solved value
  • Shows cross-multiplication and the final divide step
  • Runs a quick verification check (a·d vs b·c)
✅ Tips to avoid mistakes
  • Align units: don’t mix miles with kilometers unless you convert first.
  • Watch zeros: dividing by 0 makes the proportion undefined.
  • Keep meaning consistent: if top is “cost”, bottom should be “quantity” on both sides.
  • Check by multiplying: verify that a·d equals b·c.
❓ FAQs
  • Is a proportion the same as a ratio?

    A ratio is a comparison like a/b. A proportion is an equation that says two ratios are equal: a/b = c/d.

  • Can I use decimals?

    Yes. Decimals work perfectly in proportions. Round only at the end to avoid drift.

  • How do I check my answer fast?

    Multiply across: a·d should equal b·c (within rounding). This page shows that cross-check automatically.

  • Why does cross-multiplication work?

    Because multiplying both sides of an equation by the same nonzero value preserves equality, while removing denominators.

Educational note: For high-stakes use (medical dosing, engineering), verify inputs and follow professional standards.