Ratio Calculator

Using a ratio calculator is straightforward. Most calculators on this page ask you to enter two or more values and then choose what you want to do with them: simplify, scale, find a missing value, and so on.

Here's the general flow:

1. Enter the known values in the input fields (labeled A, B, or more parts depending on the ratio type).
2. Select the operation you need, such as simplify, find equivalent ratio, or scale up.
3. Click Calculate and the result appears instantly.

If you're not sure which calculator to use, the sections below describe each one. Start with the problem you have, find the matching section, and the calculator there will handle the math.

Simplifying a ratio means reducing it to its lowest terms, the same idea as simplifying a fraction. You divide both sides by their greatest common divisor (GCD) until no whole number other than 1 divides evenly into both.

For example, the ratio 12:8 simplifies to 3:2 because the GCD of 12 and 8 is 4. Divide both sides by 4 and you're done.

To simplify a ratio manually:

1. Find the GCD of the two numbers.
2. Divide both parts of the ratio by that GCD.
3. Check that the resulting numbers share no common factor greater than 1.

The calculator handles this automatically. Just enter your ratio and it returns the simplified form. This is especially useful when you're working with large or awkward numbers and want a cleaner expression to work with.

Two ratios are equivalent when they represent the same relationship, just scaled up or down. The ratio 1:2 is equivalent to 3:6 and 50:100 because they all reduce to the same simplified form.

The equivalent ratio calculator lets you generate ratios that match a given one. Enter your base ratio and a multiplier (or a target value for one side), and the calculator fills in the rest.

This comes up a lot in cooking. If a recipe calls for a 1:3 ratio of butter to flour and you want to make a larger batch, you need the equivalent ratio at a bigger scale. The calculator takes care of that arithmetic so you're not doing it in your head mid-recipe.

You can also work backwards: enter a ratio and ask the calculator to find an equivalent one where one part equals a specific number. It solves for the other side automatically.

Scaling a ratio means multiplying or dividing both parts by the same number to get a proportionally larger or smaller version. The relationship between the parts stays exactly the same; only the size changes.

Enter your original ratio and the scale factor (or a target value for one part), and the calculator returns the scaled ratio. This works for two-part ratios as well as three or more parts.

A proportion is simply a statement that two ratios are equal: A:B = C:D. Solving ratio and proportion problems usually means one of those four values is unknown and you need to find it.

These problems appear in math classes, standardized tests, and everyday situations like adjusting a recipe, calculating speed, or figuring out how much paint you need for a room of a different size than the one you measured.

The two methods below cover the most common approaches. Both get you to the same answer; the cross multiplication method is usually faster once you're comfortable with it.

Dividing an amount by a ratio means splitting a total into parts that match the given ratio. If three people are sharing a prize of $1,200 in the ratio 1:2:3, how much does each person get?

Here's the process:

1. Add the parts of the ratio together: 1 + 2 + 3 = 6.
2. Divide the total by that sum: $1,200 ÷ 6 = $200 per part.
3. Multiply each ratio part by $200: the shares are $200, $400, and $600.

You can verify your work by adding the shares back up. They should equal the original total. The divide-by-ratio calculator does all three steps for you: enter the total and the ratio parts, and it returns each person's (or each portion's) share. This is useful for splitting costs, dividing ingredients, allocating budgets, and similar tasks.

Comparing two ratios tells you whether they're equal (proportional) or which one is larger. To compare 3:4 and 5:7, convert both to the same form and check.

The easiest approach is converting each ratio to a decimal by dividing the first part by the second:

• 3:4 = 3 ÷ 4 = 0.75
• 5:7 = 5 ÷ 7 ≈ 0.714

Since 0.75 is greater than 0.714, the ratio 3:4 is larger. You can also use cross multiplication: multiply 3 × 7 = 21 and 4 × 5 = 20. Since 21 > 20, the first ratio is bigger.

The comparison calculator does this in one step. Enter both ratios and it tells you immediately whether they're equal, or which is greater. This is useful in situations like comparing unit prices, test scores, or ingredient concentrations.

A ratio and a fraction express the same type of relationship, just written differently. The ratio 3:5 can be written as the fraction 3/5. From there, converting to a decimal or percentage is simple.

To convert a ratio to a percentage, divide the first number by the second, then multiply by 100. So 3:4 becomes (3 ÷ 4) × 100 = 75%.

Keep in mind that a ratio like 3:5 means 3 out of every 8 total parts when you're talking about proportions of a whole, which would be 3/8 as a fraction. Context matters. If you're expressing one quantity relative to another (not relative to a total), then 3:5 = 3/5 is correct. The calculator lets you specify which interpretation you need.

The core ratio formula is simple: Ratio = A : B, where A and B are any two quantities being compared. From that base, a few specific formulas cover most ratio calculations.

• Simplify: Divide both A and B by GCD(A, B).
• Scale: Multiply (or divide) both A and B by the same factor k. Scaled ratio = kA : kB.
• Solve for missing value: If A:B = C:D, then D = (B × C) / A.
• Divide a total T by ratio A:B: Each part = T / (A + B). Share for A = A × [T / (A + B)].
• Compare ratios A:B and C:D: Cross multiply. If A × D > B × C, then A:B > C:D.

These formulas aren't complicated individually, but it's easy to mix them up when you're in the middle of a problem. Using a calculator removes the risk of arithmetic errors, especially when you're working with decimals or larger numbers. That said, knowing the underlying formulas helps you set up the problem correctly before you enter anything.

A few worked examples make the concepts concrete.

Example 1: Simplify 36:48
GCD of 36 and 48 is 12. Divide both sides: 36 ÷ 12 = 3, 48 ÷ 12 = 4. Simplified ratio: 3:4.

Example 2: Scale 2:3 up by a factor of 5
Multiply both parts by 5: 2 × 5 = 10, 3 × 5 = 15. Scaled ratio: 10:15 (which simplifies back to 2:3).

Example 3: Find the missing value in 4:9 = 20:x
Cross multiply: 4x = 9 × 20 = 180. Divide: x = 180 ÷ 4 = 45.

Example 4: Divide $500 in the ratio 3:2
Total parts: 3 + 2 = 5. Each part: $500 ÷ 5 = $100. Shares: $300 and $200.

Example 5: Compare 5:8 and 3:5
Cross multiply: 5 × 5 = 25, 8 × 3 = 24. Since 25 > 24, ratio 5:8 is larger.

Ratios are one of those math concepts that actually shows up constantly outside of school. Once you start noticing them, they're everywhere.

• Cooking and baking: Recipes are basically a set of ratios. Bread dough, cocktail mixes, spice blends. Scale a recipe up or down and you're working with equivalent ratios.
• Finance: Debt-to-income ratio, price-to-earnings ratio, current ratio for business liquidity. These numbers drive major financial decisions.
• Maps and scale models: Every map has a scale ratio. Architectural and engineering models use ratios to represent real dimensions at a workable size.
• Photography and screen design: Aspect ratios (like 16:9 for widescreen video) determine how images and interfaces are displayed across different devices.
• Medicine and pharmacy: Medication dosages are often calculated as ratios relative to body weight. Mixing concentrations in a lab also depends on accurate ratios.
• Sports statistics: Win-loss ratios, batting averages, and goal-to-shot ratios are all ways of expressing performance as a proportion.
• Construction and carpentry: Slope ratios (rise over run), material mixing ratios for concrete or mortar, and load-bearing calculations all rely on ratios.

The math behind ratios isn't complicated, but getting it wrong in any of these fields can mean a failed recipe, a miscalculated dose, or a structure that doesn't hold. That's why having a reliable calculator matters, even for problems that seem simple on the surface.