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Ratio Calculator

Find the missing number when two ratios are equal, or simplify a ratio to the smallest whole numbers that mean the same thing.

Level: Grade 6

  • Common Core standard 6.RP.A.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • Common Core standard 6.RP.A.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Printable worksheet

Ratio Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Calculation

Result

Step-by-step solution

  1. Write both ratios as fractions that are equal, with D as the missing number

    34=15D

  2. Cross-multiply: the first top number times D equals the first bottom number times the second top number

    3×D=4×15=60

  3. Divide both sides by the first top number to get D on its own

    D=603=20

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find a missing number in a ratio, or simplify a ratio to its smallest whole numbers. A ratio compares two amounts. For example, 3 : 4 means three parts of one thing for every four parts of another. Two ratios are "in proportion" when they make the same comparison, as 3 : 4 and 15 : 20 do.

This calculator does the two jobs people need most. It can scale a ratio up or down to find a missing value. It can also shrink a ratio to the smallest whole numbers that mean the same thing.

Where it's used

Why this math matters outside the classroom:

  • Screen shapes. A 1920 by 1080 screen simplifies to a 16:9 ratio by dividing both numbers by 120.
  • Concrete mixes. A 1:2:3 mix of cement, sand and gravel uses 2 buckets of cement with 4 of sand and 6 of gravel.
  • Class sizes. A school with 450 students and 18 teachers has a 25:1 student-to-teacher ratio.
  • Mixing drinks. A concentrate mixed 1:4 with water needs 500 mL of concentrate for 2 L of water.
  • Bike gears. A bike with a 48-tooth front ring and a 16-tooth rear cog has a 3:1 gear ratio, so the wheel turns 3 times per pedal turn.

Grade level and standards: Grade 6; Common Core State Standards for Mathematics 6.RP.A.3, 6.RP.A.1. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose whether to find D in A : B = C : D, or to simplify A : B.
  2. Enter A and B. To find D, also enter C, the number that matches A in the second ratio.
  3. Read D. Or read the simplified ratio, along with its decimal value and its 1 : n form.

What the inputs mean

A
The first number of the ratio you know. It can't be zero when you're finding D, because the calculator divides by it.
B
The second number of the ratio you know.
C
The number in the second ratio that matches A. The calculator finds the number that matches B.

Formula and method

A : B = C : D means A × D = B × C
D = B × C ÷ A
simplified = (A ÷ g) : (B ÷ g), where g = greatest common divisor

A and B are the two numbers of the ratio you know. C is the matching first number of the second ratio, and D is the missing one. Two ratios are equal when their cross-products are equal. That means A times D equals B times C. Rearranging that for D gives the missing number directly.

To simplify, any decimals are first turned into whole numbers by multiplying both by the same 10, 100 or 1,000 (2.5 : 1 becomes 25 : 10). Then both numbers are divided by g, their greatest common divisor. That's the biggest number that divides both evenly. Here it leaves 5 : 2.

Worked example

A screen has a 16 : 9 shape and is 1,920 pixels wide. How tall is it?

  1. Set up the proportion: 16 : 9 = 1920 : D.
  2. Cross-multiply: D = 9 × 1920 ÷ 16.
  3. Work it out: 17,280 ÷ 16 = 1,080.

Result: The screen is 1,080 pixels tall. Simplifying 1920 : 1080 gives back 16 : 9.

Understanding the result

A simplified ratio keeps the same proportion with the smallest whole numbers possible. That makes ratios easier to compare at a glance.

The 1 : n form tells you how much of the second amount there is for each single unit of the first. It's handy for mixing instructions and map scales.

Assumptions and limitations

  • All numbers are zero or positive. Ratios here compare amounts, so there are no minus signs.
  • Decimals are simplified exactly, by turning them into whole numbers, not by rounding.
  • It only handles ratios with two numbers. For a three-part ratio such as 2 : 3 : 5, work on one pair at a time.
  • Numbers with more than ten decimal places can't be simplified exactly. The calculator tells you so instead of guessing.
  • A and B can't both be zero when simplifying, since 0 : 0 doesn't describe any proportion.

Frequently asked questions

Is a ratio the same as a fraction?

They're close cousins. The ratio 3 : 4 can be written as the fraction 3/4 when you compare the first part with the second. But a ratio can also be read as parts of a whole. In 3 : 4, the first part is 3/7 of the total, not 3/4.

Does the order of a ratio matter?

Yes. 3 : 4 and 4 : 3 make opposite comparisons. Keep the amounts in the same order on both sides of a proportion.

How do I split an amount in a given ratio?

Add the parts to get the number of shares. Divide the amount by that total, then multiply by each part. To split 70 in the ratio 3 : 4, there are 7 shares of 10, so the pieces are 30 and 40.

Can a ratio contain decimals?

Yes, but whole numbers are usually clearer. Multiply both numbers by the same 10, 100 or so, then simplify: 0.1 : 0.3 becomes 1 : 3.

How this calculator is checked

Method: Cross-multiplication property of proportions; reduction by the greatest common divisor (Euclidean algorithm). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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