Ratio Calculator

Advanced Math Ratio Calculator

Three powerful ratio tools in one place

Find the simplest form, fraction, and percentage.

Enter Ratio (A : B)

Please enter valid numbers.

Leave exactly one field blank to solve it.

Leave exactly ONE field blank.

Divide a total number by a multi-part ratio.

Total Amount

Ratio Format (use colons)

Invalid format. Check numbers.

This Ratio Calculator is split into three dedicated modules to handle different mathematical needs:

Ratio Simplification: It takes any two numbers and reduces them to their smallest possible whole-number form. It also provides the fraction, decimal equivalent, and percentage.
Proportion Solver (Missing Value): If you have two equal ratios but are missing one piece of the puzzle (e.g., 4:8 = 10:?), this tool uses cross-multiplication to find the answer instantly.
Total Amount Division: This is perfect for business and finance. If you need to divide a sum of money or a physical quantity among multiple people based on a specific ratio (like 2:3:5), this tool calculates the exact share for each part.

This Ratio Cacuator is designed to be intuitive. Here is a step-by-step guide for each function:

Navigate to the Simplify Ratio box.
Enter your first number in Value A and your second number in Value B.
Click “Simplify Ratio.”
The result will show the reduced ratio, along with helpful conversions like percentages and decimals.

Look at the Solve Missing Value box. You will see four inputs arranged as A : B = C : D.
Enter the three values you already know.
Leave exactly one field blank (this is the value you want to find).
Click “Calculate Missing.” The tool will fill in the blank for you.

Go to the Divide Amount box.
In the Total Amount field, enter the full number you want to split (e.g., 5000).
In the Ratio Format field, type your ratio using colons (e.g., 1:2:3).
Click “Divide Total.” The tool will list exactly how much each “share” is worth.

Problem: You have a ratio of 24 : 36 and want to find its simplest form.
How to solve: Enter 24 in Value A and 36 in Value B in the Simplify Ratio box.
Result: The calculator will show 2 : 3. It also tells you that 24 is 66.67% of the total.

Problem: If 5 apples cost $10, how much will 12 apples cost?
Set up the proportion: 5 : 10 = 12 : X
How to solve: In the Solve Missing Value box, enter:
- A = 5, B = 10, C = 12.
- Leave D blank.
Result: The calculator will instantly show that D = 24. So, 12 apples cost $24.

Problem: Two partners, Ali and Sara, invest in a business in a ratio of 2 : 3. They made a profit of $5,000. How much does each person get?
How to solve: In the Divide Amount box:
- Enter Total Amount = 5000.
- Enter Ratio = 2:3.
Result: The calculator will show:
- Share 1 (Ali): $2,000
- Share 2 (Sara): $3,000

Problem: A standard concrete mix ratio is 1 : 2 : 4 (Cement : Sand : Gravel). You need to make 700 kg of the mix. How much of each material do you need?
How to solve: Use the Divide Amount box:
- Total Amount = 700.
- Ratio = 1:2:4.
Result:
- Cement = 100 kg
- Sand = 200 kg
- Gravel = 400 kg

Have you ever wondered how these calculations happen? Here is the “behind the scenes” logic used by the calculator:

The GCD Method (Simplification): To simplify a ratio, the calculator finds the Greatest Common Divisor (GCD). This is the largest number that divides into both parts without leaving a remainder. By dividing both sides by the GCD, we get the simplest form.
Cross-Multiplication (Solving): To solve proportions, the tool uses the algebraic rule that in a true proportion ( $A / B = C / D$ ), the product of the means equals the product of the extremes ( $A \times D = B \times C$ ). It rearranges this formula to isolate and solve for the empty box.
The Sum of Parts (Dividing): To divide a total, the calculator first adds all the numbers in your ratio together (the “Sum of Parts”). It then divides the Total Amount by this sum to find the value of a “single unit.” Finally, it multiplies that unit value back by each number in your ratio.