The Scientific Calculator

Ratio Calculator

A ratio compares two quantities. Simplify it, scale it, or convert it to a fraction - all shown step by step.

Last updated: August 2026 · Written and verified by Akash Pandey

Calculate with ratios

GCD

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This runs the same calculation engine as the main scientific calculator, entirely in your browser. Nothing you type is sent anywhere.

What is a ratio?

A ratio compares two or more quantities. Written as a : b, it tells you how much of one thing there is relative to another. A recipe calling for 2 cups of flour to 3 cups of sugar has the ratio 2:3.

Why scaling both parts equally preserves the ratio

A ratio describes a relationship, not fixed amounts - 2:3 and 200:300 describe exactly the same balance between the two quantities, because multiplying both parts by the same number scales the picture up without changing its shape. This is the same idea as an equivalent fraction: 2/3 and 200/300 are the same value. Simplifying a ratio just runs this in reverse, dividing both parts by their greatest common divisor (GCD) to find the smallest whole-number form that describes the same relationship.

a : b → (a ÷ GCD) : (b ÷ GCD)

  • Scaling up works the same way in reverse: multiply both parts by the same factor.
  • Multiplying only one part changes the relationship, not just its size - this is the most common ratio mistake.

Worked examples

  1. Simplify the ratio 8 : 12

    8 : 12

    1. Find the GCD of 8 and 12, which is 4.
    2. Divide both parts by 4: 8 ÷ 4 = 2 and 12 ÷ 4 = 3.
    3. The simplified ratio is 2 : 3.

    = 2 : 3

  2. A recipe uses flour and sugar in a 2:3 ratio. Scale it up to 20 cups total.

    2 : 3 → ? : ? (total 20)

    1. Given: the ratio 2:3, and a target total of 20 (not a target for one part).
    2. Method: find the scale factor by dividing the target total by the current total.
    3. Calculation: 20 ÷ (2 + 3) = 4. Multiply both parts by 4: 2 × 4 = 8, 3 × 4 = 12.
    4. Interpretation: 8 cups flour to 12 cups sugar keeps the same 2:3 balance but yields 20 cups total.

    = 8 : 12

  3. Which is a stronger mix: 3:4 (cleaner to water) or 6:9?

    3/4 vs 6/9

    1. Given: two ratios to compare directly against each other.
    2. Method: convert each to a decimal (part ÷ whole of the pair) so they share a common scale.
    3. Calculation: 3 ÷ 4 = 0.75; 6 ÷ 9 ≈ 0.667.
    4. Interpretation: 3:4 is the stronger mix (more cleaner relative to water) even though 6:9 uses bigger numbers - a common trap is assuming larger numbers mean a stronger ratio.

    = 3:4 is stronger (0.75 > 0.667)

Ratio to fraction

A ratio a : b can be written as the fraction a / (a + b). So 2:3 means 2/5 of the whole is the first part and 3/5 is the second.

Real-world uses

  • Recipes and mixing - concrete, paint, cocktails and cleaning solutions are all specified as ratios (e.g. a 1:4 bleach solution), and scaling a recipe up or down means scaling every part by the same factor.
  • Maps and scale drawings - a map scale of 1:25,000 means 1 cm on paper is 25,000 cm (250 m) in reality; an architect's 1:100 drawing works the same way.
  • Aspect ratios - a 16:9 screen is wider relative to its height than a 4:3 screen, regardless of the screen's actual size in inches.
  • Splitting a bill or profit share - dividing £1,000 in a 2:3 ratio between two people gives £400 and £600, using exactly the ratio-to-fraction method above.

Frequently Asked Questions

What is the difference between a ratio and a fraction?

A ratio compares two quantities to each other (a:b); a fraction represents one part of a whole (a/b). They are related: a ratio a:b means the first part is a/(a+b) of the total.

How do I simplify a ratio?

Find the greatest common divisor (GCD) of both numbers and divide each by it. For example, 8:12 has GCD 4, so the simplified form is 2:3.

Can ratios have more than two parts?

Yes. A ratio like 2:3:5 compares three quantities. To simplify, find the GCD of all three numbers.

I doubled one ingredient in a recipe and the result tastes wrong - why?

Scaling a ratio requires multiplying every part by the same factor. Doubling just one ingredient (say, the flour) while leaving the others unchanged is not scaling the ratio at all - it creates a different ratio entirely.

How do I tell which of two ratios is "stronger" or "bigger"?

Convert both to the same form (a decimal, or a fraction over a common denominator) rather than comparing the raw numbers - 6:9 looks bigger than 3:4 but is actually a weaker ratio (0.667 vs 0.75). Bigger numbers do not mean a bigger ratio.

What is the golden ratio?

The golden ratio is approximately 1.618:1. It appears in nature, art, and architecture. Two quantities are in the golden ratio if their ratio equals the ratio of their sum to the larger quantity.

Are ratios the same as proportions?

A ratio compares two quantities; a proportion states that two ratios are equal. For example, 2:3 = 4:6 is a proportion because both ratios simplify to the same value.

How does a map scale like 1:25,000 actually work?

It means one unit of distance on the map equals 25,000 of the same unit in reality - 1 cm on the map is 25,000 cm (250 m) on the ground. To find a real-world distance, measure on the map and multiply by 25,000.