Ratio Of 2 Numbers Calculator - Simplify, Scale, Find

A ratio of 2 numbers is the simplest way to compare two quantities, written A:B and read 'A to B'. Use this calculator when you need to reduce 12:18 to 2:3, scale 3:4 up to 15:20, write a ratio in the 1:n or n:1 form, or solve for the missing term in a proportion such as 3:4 = 9:D. The underlying engine uses the greatest common divisor of the two numbers, so the answer always comes back in the smallest whole numbers that preserve the original relationship.

• • Simplify a recipe ratio: Halve 200 g of butter and 800 g of flour down to 1:4 so the same recipe scales cleanly.
• • Scale a map or model ratio: Convert a 1:50,000 ratio into 1:n or n:1 form to compare it directly with another scale.
• • Solve a proportion: Find the missing fourth term of 3:4 = 9:D without doing cross multiplication by hand.
• • Compare ingredients or measurements: Reduce 12:18 to 2:3 so a buyer or chef can read the proportion at a glance.

Ratios show up in recipes, fuel mixtures, gear sets, and classroom word problems. The hard part is keeping the numbers in their simplest form so the proportion is not distorted by sloppy arithmetic. The GCD step handles that, and the dropdown lets you switch between simplify, normalize, scale, and missing-term operations. Fraction strings like 1/2 in A or B are parsed to decimals before that step runs.

If you also need a wider calculator with percentage-style ratio work alongside simplification, Ratio Calculator gives that broader view.

A single engine runs under every operation: it reduces both source terms by their GCD. Every other output - the 1:n form, the scaled ratio, the missing term - is derived from that single reduction step.

• A: First source number of the ratio. Any non-zero real number; decimal inputs are scaled up to whole numbers.
• B: Second source number of the ratio. Must be non-zero so the ratio is defined.
• GCD(A, B): Largest positive integer that divides both without a remainder. Found with the Euclidean algorithm.
• k: Scale factor for scale-up and scale-down. Must be positive and non-zero.
• C, D: Known third and fourth terms of the proportion A:B = C:D.

The Euclidean algorithm finds the GCD by replacing the larger number with the remainder of dividing it by the smaller number, until the remainder is zero. The last non-zero remainder is the GCD. For 12 and 18 the steps are 18 mod 12 = 6, then 12 mod 6 = 0, so the GCD is 6.

For the equivalent-ratio operation, the calculator uses cross multiplication instead of the GCD. The unknown term equals the diagonal product divided by the known term. According to Wikipedia, dividing both terms of a ratio by their GCD yields the same proportion in lowest integer terms, which is why one engine covers all six operations.

According to Wikipedia, Ratio, dividing both terms of a ratio by their GCD yields the same proportion in lowest integer terms.

When the source ratio has three parts instead of two, Simplify Ratio Calculator applies the same GCD reduction to 3-part ratios.

Four ideas carry the ratio of 2 numbers calculator. Together they explain why a simplified ratio is useful.

If you understand these four ideas, the rest of the calculator is just choices about which output to display. Simplify uses GCD directly, the 1:n and n:1 forms are ratios after dividing through, the scale operations are multiplication and division by k, and the missing-term operation uses cross multiplication.

Decimals like 0.6 and 0.8 are scaled to whole numbers before the GCD step, which is why 0.6:0.8 reduces to 3:4. The A and B fields also accept fraction strings such as 1/2 or 3/4; the parser turns those into 0.5 and 0.75 so the same GCD step produces 2:3.

For proportion problems focused on the missing term rather than the simplified form, Equivalent Ratio Calculator solves a:b = c:d directly.

Using the ratio of 2 numbers calculator takes four short steps once you know which operation you need. The dropdown controls which outputs are emphasized, but the inputs are the same for every operation.

1. 1 Pick the operation: Choose Simplify, 1:n form, n:1 form, Make k times larger, Make k times smaller, or Find an equivalent ratio from the Operation dropdown.
2. 2 Enter A and B: Type the two source numbers of the ratio in the First number (A) and Second number (B) fields. Decimals and fraction strings such as 1/2 or 3/4 are accepted; both terms must be non-zero.
3. 3 Add k, C, or D when needed: If you are scaling, type the positive scale factor k. If you are solving a proportion, type the known third term C or fourth term D and leave the other at zero.
4. 4 Read the results: The Result row shows the simplified, normalized, scaled, or missing-term answer; the secondary rows show simplified A, simplified B, GCD, and any operation-specific form.
5. 5 Reset for a new ratio: Press the Reset button to clear the form and return to the default 12:18 example.

Practical use: a baker scales a recipe from 12:18 (butter to flour) to a single loaf. With operation = Simplify, A = 12, B = 18, the Result row shows 2 : 3 and the GCD row shows 6, so the baker can multiply by any batch size.

When the ratio describes triangle sides or angles rather than two free numbers, Triangle Ratio Calculator turns a:b = c:d into a side or angle.

A dedicated ratio of 2 numbers calculator is faster than redoing the arithmetic by hand. Every common operation is one dropdown choice away.

• • Lowest terms without pencil work: Dividing by the GCD is done for you, so 24:36 reduces to 2:3 instantly.
• • Switchable output forms: Six operations cover every common ratio task from simplification to missing-term solving on one page.
• • Decimal and fraction safe: Decimals like 0.6 and 0.8 are scaled to whole numbers before simplification; fraction strings like 1/2 are parsed to decimals first.
• • Transparent GCD display: The greatest common divisor is shown alongside the simplified ratio so the arithmetic can be checked.
• • Proportion solving built in: Cross multiplication is applied automatically, so 3:4 = 9:D gives D = 12 with no setup.
• • Mobile friendly layout: Inputs collapse to one column on phones, so the calculator works at a kitchen counter or in a classroom.

These benefits line up with the tasks the page is designed for. Most people visit because they need an answer in a hurry, and the dropdown plus the always-visible inputs keep the cognitive load low.

For ratios that carry a sign along a line - dividing a segment internally or externally with a signed ratio - Ratios of Directed Line Segments Calculator applies the same A:B = C:D rule to point positions.

A few small factors decide what the calculator returns for any given A and B.

• • A ratio with B equal to zero is undefined, so the calculator rejects zero inputs. Enter a small positive number if you want to see how close the ratio gets to zero.
• • Very precise decimals are rounded to the nearest representable integer during scaling. For ratios needing more than six significant digits, simplify by hand.
• • The equivalent-ratio operation assumes a single missing term. If both C and D are non-zero, the calculator uses D as the known term.

These factors matter most when inputs come from a measurement rather than a clean integer. A kitchen scale that reads 200.4 g and 800.1 g will reduce to a ratio that is almost but not exactly 1:4. If that matters, round the inputs to whole grams first.

According to Wolfram MathWorld, Ratio, equivalent ratios are scalar multiples of each other, and the 1:n form normalizes the proportion to one variable.

When the simplified ratio happens to be 1.618 to 1, Golden Ratio Calculator checks whether your pair matches phi.