# Equivalent Ratio Calculator

Find equivalent ratios, scale ratios up or down, and generate lists of equivalent ratios. Free online ratio calculator for math, cooking, and more.

## What this calculates

Find equivalent ratios by scaling a ratio up or down. Enter your ratio and a multiplier or target value to instantly see equivalent ratios. Great for recipes, scale models, and math homework.

## Inputs

- **First Value (A)** — The first part of the ratio.
- **Second Value (B)** — The second part of the ratio.
- **Multiplier / Scale Factor** — Multiply both parts of the ratio by this number.
- **Target Value for A** — Find the equivalent ratio where the first value equals this number.

## Outputs

- **Simplified Ratio** — formatted as text — The ratio reduced to its simplest whole-number form.
- **Scaled Ratio** — formatted as text — The ratio multiplied by the scale factor.
- **Equivalent Ratio (Target A)** — formatted as text — The equivalent ratio where A equals the target value.
- **Equivalent Ratios (x1 to x10)** — formatted as text — A list of the first 10 equivalent ratios.

## Details

Two ratios are equivalent if they represent the same relationship between quantities. For example, 2:3 and 4:6 are equivalent because both simplify to the same proportion.

**How Equivalent Ratios Work:**

You create an equivalent ratio by multiplying (or dividing) both parts by the same number. Starting with 3:5, you can multiply both by 2 to get 6:10, or by 3 to get 9:15. All three ratios are equivalent.

**Finding an Equivalent with a Target:**

If you need the first value to equal a specific number, divide that target by the original first value to get the scale factor, then multiply both parts. For instance, to find the equivalent of 2:7 where the first value is 10: scale factor = 10/2 = 5, so the equivalent ratio is 10:35.

**Where Equivalent Ratios Show Up:**

Recipes are a perfect example. If a recipe calls for 2 cups of flour to 3 cups of sugar and you want to use 6 cups of flour, you need the equivalent ratio 6:9. Map scales, unit conversions, and proportion problems all rely on equivalent ratios.

## Frequently Asked Questions

**Q: What are equivalent ratios?**

A: Equivalent ratios express the same relationship between two quantities. For example, 1:2, 2:4, and 5:10 are all equivalent because dividing the second number by the first always gives 2. You create equivalent ratios by multiplying or dividing both parts by the same non-zero number.

**Q: How do I find an equivalent ratio with a specific value?**

A: Divide your target value by the corresponding original value to get the scale factor. Then multiply both parts of the original ratio by that factor. For example, to scale 3:4 so that the first part equals 12: factor = 12/3 = 4, so the equivalent ratio is 12:16.

**Q: What is the difference between a ratio and a proportion?**

A: A ratio compares two quantities (like 3:5), while a proportion is an equation stating that two ratios are equivalent (like 3:5 = 6:10). Proportions are used to solve for unknown values when you know three of the four numbers.

**Q: Can equivalent ratios have decimals?**

A: Yes, equivalent ratios can include decimals. For example, 1.5:2.5 is equivalent to 3:5 (multiply both by 2). This calculator handles decimal inputs and simplifies them to whole numbers when possible.

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Source: https://vastcalc.com/calculators/math/equivalent-ratio
Category: Math
Last updated: 2026-04-08