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Ratio Calculator

Simplify a ratio, scale it to a new value, and see it as a decimal — instantly in your browser. Enter two numbers and an optional target to scale to.

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Quick Answer

Enter two numbers — A and B — and the tool shows the ratio simplified to its lowest terms, the matching B when you scale A to a new value, and the ratio as a decimal. So 16 to 9 scaled to 1920 gives 1080 — the 1920 by 1080 of a Full HD screen. It runs entirely in your browser.

What the Ratio Calculator Does

This tool works with a ratio three ways: it reduces it to its simplest whole-number form, it scales it so that A becomes a value you choose and finds the matching B, and it gives the ratio as a single decimal.

It is the quick way to simplify a proportion, resize while keeping an aspect ratio, or convert a ratio into a number you can compare — useful for screens, recipes, mixes and maps.

How It Works

To simplify, the tool finds the greatest common divisor of the two numbers — the largest value that divides both — and divides each by it, giving the ratio in its lowest terms. To scale, it keeps the proportion fixed: if A becomes your target value, the matching B is the target multiplied by B and divided by A. The decimal is simply A divided by B.

So 16 to 9 is already in lowest terms; scaling 16 to 1920 multiplies the proportion up to give 1080; and the decimal is 16 divided by 9, about 1.778 — the familiar widescreen aspect ratio expressed as a number.

Methodology

  1. Read the two numbers. Take A and B, and the value you want to scale A to.
  2. Simplify with the GCD. Divide both numbers by their greatest common divisor for the lowest terms.
  3. Scale proportionally. Find the matching B when A becomes your target value.
  4. Give the decimal. Divide A by B to express the ratio as a single number.

Ratio calculations

simplified = A ÷ gcd(A, B) : B ÷ gcd(A, B) scaled B = target × B ÷ A decimal = A ÷ B
Worked example
16 : 9, scale A to 1920 → simplified 16:9 · scaled B 1080 · decimal 1.778

The greatest common divisor reduces the ratio to lowest terms. Scaling keeps the proportion fixed, which is how an aspect ratio like 16:9 scales to 1920 by 1080.

Assumptions

  • Simplification works cleanly with whole numbers; the greatest common divisor reduces them to lowest terms.
  • Scaling keeps the proportion exactly, so the matching value is found by keeping A-to-B constant.
  • The first number (A) must not be zero, since the scaling and decimal both divide by it.

Standards & references

  • Greatest common divisor — The largest number that divides two values evenly. Dividing both parts of a ratio by it reduces the ratio to its simplest whole-number form.
  • Proportion — Two ratios are equal when they represent the same proportion. Scaling A to a new value and finding the matching B preserves that proportion.
  • Ratio as a decimal — Dividing the first part by the second turns a ratio into a single number, which is easy to compare — for example 16 to 9 is about 1.778.

Accuracy & Limitations

The simplified ratio, the scaled value and the decimal are computed exactly from the numbers you enter, so the results are precise.

Simplification is cleanest with whole numbers. Decimal inputs still produce a decimal ratio, but the lowest-terms simplification is designed for integer ratios, where the greatest common divisor applies neatly.

Scaling keeps the proportion exact, which can give a non-whole matching value if the numbers do not divide evenly — that is correct, just not always a round number.

The first value must not be zero, because the decimal and the scaling both divide by it. A zero there has no meaningful ratio or scale.

Real-World Use Cases

Aspect ratios

Scale a screen or image ratio like 16:9 to a width and find the height.

Simplifying proportions

Reduce a ratio to its lowest terms.

Recipes and mixes

Scale a ratio of ingredients up or down.

Comparing ratios

Turn ratios into decimals to compare them.

When to use it — and when not to

Good for

  • Simplifying a ratio to lowest terms
  • Scaling a ratio (aspect ratios)
  • Getting a ratio as a decimal
  • Resizing while keeping a proportion

Not the best choice for

  • Three-part ratios (A:B:C)
  • Percentages or shares of a total
  • Unit conversions
  • Odds or probability ratios

For a share of a total, use a percentage calculator. For three-part ratios, split the calculation into pairs. This tool simplifies, scales and converts a two-number ratio.

Frequently Asked Questions

How does it simplify a ratio?
It finds the greatest common divisor of the two numbers — the largest value dividing both — and divides each by it. So 16 to 8 simplifies to 2 to 1, and 16 to 9 is already in lowest terms.
How does scaling work?
It keeps the proportion fixed. When you set A to a new value, the matching B is that value multiplied by B and divided by A. Scaling 16 to 1920 in a 16:9 ratio gives 1080.
Why is 16:9 useful as 1920 by 1080?
Because 1920 by 1080 is a 16:9 ratio — the standard Full HD screen shape. Scaling 16:9 up by 120 gives 1920 by 1080, which is why the tool is handy for aspect ratios.
What does the decimal mean?
It is the first number divided by the second, turning the ratio into a single value. For 16 to 9 that is about 1.778, which lets you compare ratios as plain numbers.
Can it handle decimals as inputs?
It accepts them and gives a decimal ratio, but the lowest-terms simplification is intended for whole numbers, where the greatest common divisor applies cleanly.
Can it do three-part ratios like 2:3:5?
Not directly — it works with two numbers. For a three-part ratio, simplify or scale it in pairs, or use the proportions of the total separately.
What if A is zero?
The scaling and decimal both divide by A, so a zero there has no valid result. Enter a non-zero first value for a meaningful ratio.
How is this different from a percentage?
A ratio compares two parts to each other; a percentage compares a part to a whole. To express a ratio as a share of the total instead, a percentage calculator is the right tool.
Can I scale down as well as up?
Yes. Set A to a smaller value than its original and the matching B scales down proportionally, keeping the same ratio.
Does the order of A and B matter?
Yes for the decimal and the scaling, since both divide by A. The simplified ratio reads in the order you enter, so 16:9 and 9:16 are different orientations.
Is my data uploaded?
No. The calculation runs entirely in your browser. Nothing is sent to a server.
What is an everyday use for the decimal?
Comparing shapes or proportions. A 16:9 screen is about 1.78 and a 4:3 screen is about 1.33, so the decimals show at a glance that 16:9 is wider.

References

Simplifies a ratio to its lowest terms using the greatest common divisor and scales it proportionally; the decimal is the first value divided by the second.

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