Ratio Calculator

A ratio compares two quantities by division, telling you how much of one thing there is for every unit of another. Written a : b (read "a to b"), it captures relationships like 3 parts cement to 4 parts sand, or a screen that is 16 units wide for every 9 units tall. This calculator does three jobs with that idea: it simplifies a ratio to its smallest whole-number form, it scales a ratio up or down by a chosen factor, and it solves a proportion by finding the missing fourth value when three are known. Each mode shows the working so you can follow the maths, not just copy the answer.

It is built for everyday practical use: students checking homework on equivalent fractions and proportions, cooks adjusting a recipe for more servings, designers matching aspect ratios, investors splitting an amount between assets, and builders mixing concrete or paint. Anywhere two or more quantities need to stay in a fixed relationship, a ratio is the tool, and this page covers the most common operations you will perform on one.

Simplifying a ratio

To reduce a : b to lowest terms, divide both numbers by their GCF — the Greatest Common Factor (also called GCD, the largest whole number that divides both exactly). For example 6 : 9 has a GCF of 3, so dividing both sides gives 2 : 3. The simplified ratio is equivalent to the original because dividing both quantities by the same number does not change their relationship. When the inputs are decimals, first multiply both by 10, 100, or 1000 to turn them into whole numbers, then take the GCF — that is exactly what this calculator does internally before it reduces.

Equivalent ratios and scaling

Two ratios are equivalent when one can be obtained from the other by multiplying or dividing both terms by the same non-zero number. So 2 : 3, 4 : 6, 6 : 9, and 20 : 30 all describe the identical relationship. Scaling applies this directly: to enlarge a ratio, multiply both terms by the scale factor; to shrink it, multiply by a fraction. The scale mode keeps the proportion intact while changing the absolute size, which is exactly what you need when doubling a recipe or resizing a layout.

Dividing a quantity in a given ratio

A frequent task is sharing a total amount in a ratio rather than equally. The trick is to add the parts to get the total number of shares, then give each side its fraction of the whole. For a ratio a : b applied to a total T, side A receives a / (a + b) × T and side B receives b / (a + b) × T. For instance, splitting ₹2000 between two people in the ratio 3 : 2 means 5 shares in all: the first gets 3/5 × 2000 = ₹1200 and the second gets 2/5 × 2000 = ₹800, and 1200 + 800 = 2000 as a check.

Proportions and solving for the unknown

A proportion is a statement that two ratios are equal: a : b = c : d, which is the same as the equation a/b = c/d. When one of the four values is missing, you find it by cross-multiplication, since a/b = c/d rearranges to a × d = b × c. Solving for the fourth term gives d = (b × c) / a. This is the engine behind the Solve Proportion mode, and the tool also verifies the answer by confirming both ratios reduce to the same decimal.

Worked example

A map uses a scale where 2 cm represents 5 km. How many kilometres does 9 cm represent? Set up the proportion 2 : 5 = 9 : d, so d = (5 × 9) / 2 = 45 / 2 = 22.5 km. You can check it by reducing both sides: 2/5 = 0.4 and 9/22.5 = 0.4, so the proportion holds. Entering A = 2, B = 5, C = 9 in the Solve Proportion mode returns the same 22.5.

Tips

• Always simplify before comparing two ratios — it is far easier to see that 2 : 3 and 8 : 12 match once both are reduced.
• Keep the order consistent: in cement : sand = 3 : 4 the first number must always refer to cement, or the result is wrong.
• To convert a ratio to a percentage split, divide each part by the sum of the parts; 1 : 3 means 25% and 75%.

Common mistakes to avoid

• Adding instead of multiplying when scaling: to double 2 : 3 you multiply both terms to get 4 : 6, not add to get 4 : 5 — adding changes the relationship.
• Forgetting to total the shares: when dividing a quantity in ratio a : b, the denominator is a + b, not just a or b.
• Mixing up units: both terms of a ratio must be in the same unit before you simplify; compare cm with cm, not cm with metres.
• Reversing a proportion: a : b = c : d is not the same as a : b = d : c, so make sure the corresponding terms line up before cross-multiplying.