Ratio Calculator

Proportion Solver (Solve A:B = C:D):

Step 1: Select "Solve A:B = C:D" from the Calculator Mode dropdown.

Step 2: Enter any three of the four values (A, B, C, D) and leave exactly one field empty. The calculator solves for the missing value using cross-multiplication.

Step 3: Click Calculate. The result shows the missing value, the complete proportion, and step-by-step solution.

Ratio Scaler (Enlarge or Shrink):

Step 1: Select "Scale a ratio" from the Calculator Mode dropdown.

Step 2: Enter the two parts of your ratio in the Left and Right fields.

Step 3: Choose whether to Enlarge or Shrink the ratio.

Step 4: Enter the multiplier (how many times to scale it).

Step 5: Click Calculate. The result shows the scaled ratio.

A ratio is a way to compare two or more quantities by showing the relative size of one quantity to another. Written as A:B (read as "A to B"), a ratio tells you that for every A units of the first quantity, there are B units of the second quantity.

Ratios appear everywhere in daily life. A recipe that calls for 2 cups of flour to 1 cup of sugar has a 2:1 ratio. A map scale of 1:100,000 means 1 centimeter on the map represents 100,000 centimeters (1 kilometer) in real life. A classroom with 15 students and 1 teacher has a student-to-teacher ratio of 15:1.

A proportion is an equation stating that two ratios are equal: A:B = C:D. This means A/B = C/D. Cross-multiplication gives us A × D = B × C, which lets us find any missing value when the other three are known. This is the foundation of the proportion solver in this calculator.

Ratios can be scaled up or down by multiplying or dividing both parts by the same number. The ratio 3:4 is equivalent to 6:8, 9:12, and 30:40 — they all represent the same relationship. Scaling ratios is useful when adjusting recipes, resizing images, mixing solutions, or converting between measurement systems.

Proportion Solver (Cross-Multiplication):

Given A:B = C:D, the relationship is A/B = C/D, which means A × D = B × C.

To find the missing value:
- If A is missing: A = (B × C) / D
- If B is missing: B = (A × D) / C
- If C is missing: C = (A × D) / B
- If D is missing: D = (B × C) / A

Example: If 3:4 = 600:D, then D = (4 × 600) / 3 = 2400 / 3 = 800.

Ratio Scaling:

To enlarge a ratio by a factor of N, multiply both parts by N:
- A:B enlarged by N = (A × N):(B × N)

To shrink a ratio by a factor of N, divide both parts by N:
- A:B shrunk by N = (A / N):(B / N)

Example: 250:280 shrunk by 2.5 = 100:112.

Example 1: Solving a Proportion
A recipe uses flour and sugar in a 3:4 ratio. If you have 600g of flour, how much sugar do you need? Set up 3:4 = 600:D, leave D empty. Result: D = 800g of sugar.

Example 2: Scaling a Map Distance
A map has a scale of 1:25,000. A trail measures 8 cm on the map. Set up 1:25,000 = 8:D. Result: D = 200,000 cm (2 km) in real distance.

Example 3: Shrinking a Ratio
You have a paint mixture of 250:280. You need a smaller batch at half the size. Use the Scale mode, enter 250:280, select Shrink, multiplier 2. Result: 125:140.

Simplify before solving. If your ratio has large numbers, divide both sides by their greatest common divisor first. 150:200 simplifies to 3:4, making the math much easier.

Cross-multiplication is your best friend. For any proportion A:B = C:D, the relationship A×D = B×C always holds. This lets you find any missing value when you know the other three.

Check your answer by plugging it back in. After solving, verify that A/B equals C/D. If the two fractions are equal, your answer is correct.

Scaling preserves the ratio. Multiplying or dividing both sides by the same number gives an equivalent ratio. 3:4 = 6:8 = 30:40 — they all represent the same relationship.