A ratio is simply a way to compare two or more quantities by their relative sizes. If a recipe calls for 2 cups of flour and 1 cup of water, the flour-to-water ratio is 2:1. If a prize of $500 is shared between two people in a 3:2 split, one person receives $300 and the other $200. This ratio calculator does the three jobs people actually need with ratios: reducing a ratio to its lowest terms, scaling a ratio up or down to find a missing value, and dividing a total amount according to a ratio.
Type your numbers into the boxes and the result updates instantly. There is no signing up and nothing to download — pick your calculation type, enter the terms, and read the answer on the result card.
How to Use
- Choose your Calculation Type from the dropdown:
- Simplify — reduces a ratio like 6:4:8 down to 3:2:4, the smallest whole numbers that keep the same relationship.
- Scale — finds the matching real-world value. If a:b = 2:3 and you know the amount for a is $10, this tells you the amount for b is $15.
- Split — divides a total by the ratio. Splitting $500 in a 3:2 ratio gives shares of $300 and $200.
- Enter the First Term (a) and Second Term (b) of your ratio. These are required.
- Add a Third Term (c) only if you have a three-way ratio such as 2:3:5. Leave it at 0 for a normal two-term a:b ratio.
- Fill in Known Amount / Total when you are scaling or splitting. In Scale mode it is the real value that lines up with the first term; in Split mode it is the whole amount to divide up.
- Read the result card. The Greatest Common Divisor shows the number every term was divided by; the Ratio line shows the reduced a:b:c relationship; the Result lines show each scaled or split share.
The calculator works for whole-number ratios and reports the exact lowest-term form. Negative ratio terms are rejected, because a negative share of a mixture or a prize has no practical meaning.
How Ratios Are Simplified
To reduce a ratio to lowest terms, the engine finds the greatest common divisor (GCD) of all the nonzero terms and divides each term by it. Take 6:4:8. The largest number that divides 6, 4, and 8 evenly is 2. Dividing every term by 2 gives 3:2:4. The relationship is identical — for every 3 units of the first part there are 2 of the second and 4 of the third — but the numbers are as small as they can be while staying whole.
The GCD is the same idea as "largest shared factor." For 1200000:800000:1600000, the GCD is 400000, so the ratio still collapses cleanly to 3:2:4. Notice how a huge-looking ratio reduces to the exact same simple form — that is why simplifying ratios is never about the absolute size, only about the relationship between the numbers.
Scaling and Splitting
Scaling a ratio is multiplication by a common factor. If a:b = 2:3 and you know the first part corresponds to $10, the scale factor is 10 ÷ 2 = 5, so the second part is 5 × 3 = $15. Every term of the ratio is multiplied by the same factor, which keeps the relationship unchanged. This is the same arithmetic behind map scales, recipe doubling, and unit conversion.
Splitting a total works the other way around. With $500 to share in a 3:2 ratio, the total number of parts is 3 + 2 = 5. Each part is worth $500 ÷ 5 = $100. The first person gets 3 parts = $300, and the second gets 2 parts = $200. Expressed as a percentage, the first share is 60% of the total and the second is 40%. The calculator does this division for you, and it extends naturally to three-way ratios such as 2:3:5.
Examples
Example 1 — Simplifying a paint mix. A decorator mixes 12 liters of white with 8 liters of colorant, a ratio of 12:8. In Simplify mode the GCD is 4, so the reduced ratio is 3:2. Stating the mix as "3 to 2" is cleaner and makes it easy to repeat the batch at any size.
Example 2 — Scaling a recipe. A dough recipe uses flour and water in a 5:3 ratio. You have 500 grams of flour and want the matching water weight. In Scale mode, set a:b = 5:3 and the known amount 500 for the first part. The factor is 500 ÷ 5 = 100, so the water is 100 × 3 = 300 grams. The dough stays perfectly balanced.
Example 3 — Splitting a $1,000 bill. Three roommates agree to split rent in the ratio 5:3:2. In Split mode with a total of $1000, the parts sum to 10, so the shares are $500, $300, and $200. The person with the largest room pays half the total, or 50%.
Example 4 — A three-way chemical mixture. A garden spray concentrates to water in a 1:4 ratio, meaning one part concentrate to four parts water — a 20% concentrate strength. Setting a:b = 1:4 and scaling so that the first part is 100 mL gives 400 mL of water for a 500 mL batch.
FAQ
What is a ratio in math?
A ratio compares two or more quantities by their relative size, written as a:b or a:b:c. It tells you how many times one number contains another. For example, a 3:2 ratio means the first quantity is one-and-a-half times the second, or 60% versus 40% of the combined total.
How do I simplify a ratio?
Find the greatest common divisor (GCD) of all the terms and divide each term by it. For 6:4:8 the GCD is 2, giving 3:2:4. Enter your ratio in Simplify mode and the calculator does this division for you and shows the GCD it used.
How do I find a missing value in a ratio?
If a:b is a known ratio and you know the real value of a, the missing value of b equals (known value of a) × (b ÷ a). For 2:3 with a known value of $10, b = 10 × 3 ÷ 2 = $15. Use Scale mode and enter the known amount that matches the first term.
How do I divide an amount by a ratio?
Add the ratio parts to get the total number of parts, divide the total amount by that sum to find the value of one part, then multiply by each term. Splitting $500 in a 3:2 ratio: 5 parts total, $100 per part, giving $300 and $200. Use Split mode for this.
Can ratios have more than two terms?
Yes. A ratio can be a:b:c and beyond. In this calculator, fill in the optional Third Term (c) to work with three-way ratios such as 2:3:5. Leave it at 0 for an ordinary two-term ratio.
What does GCD mean on the result card?
The greatest common divisor is the largest whole number that divides every term of your ratio evenly. It is the number the calculator divided your original ratio by to reach the lowest-term form. A GCD of 1 means your ratio was already in simplest form.
Related Calculators
- Percentage Calculator — convert a ratio into a percent and back.
- Average Calculator — find the mean of a list before comparing ratios.
- Fraction Calculator — simplify and operate on fractions, the close cousin of ratios.
- Proportion / Scale Ratio — bookmark this page for repeat scaling and split tasks.
Disclaimer
This ratio calculator is provided for informational purposes only and does not constitute mathematical, financial, engineering, or legal advice. Simplified and scaled values are based on the numbers you enter; always double-check critical mixtures, payments, or construction quantities before acting. The engine assumes non-negative ratio terms and rejects negative input because negative shares have no practical interpretation in everyday ratio problems.