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Ratio Calculator

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Simplify ratios, find missing values in A:B = C:D, and split totals by ratio. Free online ratio calculator for students and professionals alike.

Reviewed by the thecalcu.com team · Last updated July 9, 2026

3
4
700

Simplified Ratio

3 : 4
Value A
Value B
A's Share
0
B's Share
0

What is a Ratio?

A ratio calculator simplifies any ratio A:B down to its lowest terms, works out the percentage share each term holds of the combined total, and splits a given total across that exact ratio. Those three operations cover almost every practical ratio problem you'll run into, verifying a recipe scale-up, dividing a business investment, or checking that a map scale makes sense.

A ratio compares two quantities by division: A:B tells you how A and B relate in size. Unlike a fraction, a ratio is built to compare two separate quantities rather than express one as part of a whole. A partnership that splits profits 3:4 means the first partner gets 3 parts for every 4 parts the second partner receives, on a combined pool of $700,000, that works out to $300,000 and $400,000.

The operation underneath every ratio problem is the GCD, the greatest common divisor. Dividing both terms by their GCD gets you the simplest form: 12:18 reduces to 2:3 (GCD = 6), and 1.5:2.5 reduces to 3:5. This calculator's step breakdown shows that simplification explicitly, which is handy when you need to show your work.

The Scale to Total field is where most people actually use this tool, enter the amount you want to distribute and get each party's exact share back immediately. That covers the most common real-world ratio task: splitting profits, costs, or a shared purchase.

For comparing two datasets over time rather than a fixed proportion, the Percentage Change Calculator is the better fit.

How to use this Ratio calculator

  1. Enter Value A, the first term of the ratio. Any positive number works, including decimals. For a 3:4 split, enter 3.
  2. Enter Value B, the second term. Order matters here: 3:4 and 4:3 are different ratios, so make sure A and B are in the order you intend.
  3. Enter Scale to Total, the amount you want divided in this ratio. The default of 700 makes a 3:4 split come out to easy round numbers (300 and 400) for a sanity check. For a real partnership split, enter the actual dollar amount.
  4. Read the ratio decimal and percentage splits, these two outputs together give you the full shape of the proportion at a glance.
  5. Expand the step breakdown, it shows the GCD calculation and the simplified ratio explicitly, useful when you need to document how you got the answer.

Why Use a Ratio Calculator?

Ratio simplification and splitting are conceptually simple but fiddly to do by hand, finding the GCD of two large numbers or dividing $123,750 by a 7:5 ratio in your head invites mistakes.

GCD simplification with the working shown. The step breakdown displays the GCD computation and resulting simplified ratio, which is exactly what's expected when you need to show your reasoning rather than just state an answer.

Instant percentage splits. "A as % of Total" and "B as % of Total" tell you each term's share of the combined whole immediately, a 3:7 ratio means A is 30% and B is 70%, and seeing that number directly makes partnership splits and budget allocations easier to interpret.

Scale-to-total for real splits. Enter $700,000 with A=3 and B=4, and you get back $300,000 and $400,000 without doing the division yourself, directly usable for accounting, legal documentation, or planning.

Who Should Use This Calculator?

Students working through ratio and proportion problems. Standard exercises, simplifying a ratio, dividing an amount by a given ratio, solving for a missing value in a proportion, are all covered here, and the step breakdown shows GCD working in the format most coursework expects.

Business partners and co-founders. Investment and profit splits in partnerships and joint ventures are almost always defined as ratios. If one partner puts in $35,000 against another's $52,500, the ratio is 35,000:52,500 = 2:3 simplified, meaning profits split 40/60. This calculator confirms both the simplified ratio and the dollar split instantly.

Finance and investment analysts. Financial ratios, P/E, debt-to-equity, current ratio, and portfolio allocation percentages are everyday inputs and outputs of fundamental analysis. Seeing a 60:40 debt-equity split as both a 1.5:1 decimal and a 60%/40% split at once speeds up the work, and the Margin Calculator is a natural next stop for margin-specific ratio work.

Anyone scaling a recipe or formulation. A recipe in a 2:3:5 ratio of flour to butter to sugar needs to scale from a 200g batch to 500g. Plug the appropriate pair into Scale to Total and get exact weights without working through the proportion by hand.

What Insights Does the Ratio Calculator Give You?

A ÷ B (Ratio) is the decimal form, how many times A fits into B. For 3:4, that's 0.75; for 5:2, it's 2.5. This figure doubles as a financial ratio directly: a current ratio of 2.5 means $2.50 of current assets for every $1 of current liabilities.

A as % of Total and B as % of Total show each term's share of the combined total (A+B), and they always sum to 100%. For 3:4, that's 42.86% and 57.14%, often the most intuitive way to read a split.

A's Share and B's Share (of Total) apply the ratio to your Scale to Total input directly. With A=3, B=4, and a total of $700,000, you get back $300,000 and $400,000, change the total and both shares update instantly, which is handy for modeling a few different scenarios in one sitting.

Formula & Methodology

Ratio decimal:
A ÷ B

A as % of total:
(A ÷ (A + B)) × 100

B as % of total:
(B ÷ (A + B)) × 100

A's share (of total T):
(A ÷ (A + B)) × T

B's share (of total T):
(B ÷ (A + B)) × T

Simplified ratio (shown in steps):
Divide both terms by GCD(A, B): simplified = (A ÷ GCD) : (B ÷ GCD)

Worked example, A = 5, B = 8, Scale to Total = $260,000:

GCD(5, 8) = 1 → already in simplest form, 5:8
A as % of total = (5 ÷ 13) × 100 = 38.46%
B as % of total = (8 ÷ 13) × 100 = 61.54%
A's share = 38.46% × 260,000 = $100,000
B's share = 61.54% × 260,000 = $160,000

A second example, simplification, A = 24, B = 36, Scale to Total = 100:

GCD(24, 36) = 12 → simplified ratio = 2:3
A as % of total = (24 ÷ 60) × 100 = 40%
B as % of total = (36 ÷ 60) × 100 = 60%

Assumptions and limitations:
- Both A and B must be positive numbers, zero or negative inputs don't produce a meaningful ratio.
- A Scale to Total of 0 gives shares of 0 by definition.
- Outputs round to 2–4 decimal places depending on the field; for averaging a series of ratios, the Average Calculator is the right companion tool.

Frequently Asked Questions

A ratio expresses the relative size of two or more quantities, written as A:B. A ratio of 3:4 means for every 3 units of A there are 4 units of B. A fraction A/B is a single number, A divided by B, always expressing A as part of B. You can convert A:B to the decimal fraction A/B, but ratio notation is built for comparing two distinct quantities, not for showing one as a portion of a whole.
Divide both terms by their greatest common divisor (GCD). GCD(12, 16) is 4, so 12:16 simplifies to 3:4. For decimals like 1.5:2.5, multiply both by 10 to get 15:25, then divide by GCD(15, 25) = 5 for 3:5. A ratio is in lowest terms once there's no common factor left between its two numbers.
To divide a total T in ratio A:B, calculate each share separately: A's share = (A ÷ (A+B)) × T, and B's share = (B ÷ (A+B)) × T. Splitting $70,000 in a 3:4 partnership gives A a share of (3 ÷ 7) × 70,000 = $30,000 and B a share of (4 ÷ 7) × 70,000 = $40,000. Enter A, B, and your total in the Scale to Total field to get both figures instantly.
A ratio compares two quantities (A:B). A proportion is a claim that two ratios are equal, A:B = C:D. Proportions let you solve for a missing value once three of the four numbers are known: if 3:4 = C:20, then C = 3 × 20 ÷ 4 = 15. Cross-multiplication (A × D = B × C) is the standard technique for solving these. Think of a ratio as a relationship and a proportion as putting that relationship to work.
Cross-multiply: A × D = B × C. If 3:4 = C:20, then 3 × 20 = 4 × C, so C = 15. If A:5 = 6:15, then 15A = 30 and A = 2. This calculator handles the ratio decimal and percentage splits directly, for missing-value proportion problems, apply cross-multiplication to whichever three values you have.
For ratio A:B, A's share of the combined total is (A ÷ (A+B)) × 100. A ratio of 3:7 gives A a 30% share and B a 70% share. If instead you want A relative to B alone, use (A ÷ B) × 100, for 3:4, that's 75%. This calculator shows both: 'A ÷ B (Ratio)' is A relative to B, while 'A as % of Total' and 'B as % of Total' give the combined-total split.
Financial ratios are core analytical tools, the current ratio (current assets to current liabilities) measures liquidity, debt-to-equity measures leverage, and P/E measures valuation relative to earnings. A current ratio of 2:1 means a business holds twice as many short-term assets as liabilities, generally read as a healthy sign. Investors and lenders lean on ratios like these constantly when comparing companies.
Yes, ratios accept any positive real numbers. A ratio of 1.5:2.5 is perfectly valid and simplifies to 3:5. You'll see decimal ratios in financial analysis (a P/E of 24.6:1) and mixing problems (2.5 liters of solution A to 3.75 liters of solution B reduces to 2:3). This calculator handles decimal inputs and simplifies them correctly in the step breakdown.
A unit ratio takes the form 1:N or N:1, where one side has been reduced to 1, it's the easiest format to reason about intuitively. A map scale of 1:100 means 1 inch on paper equals 100 inches in reality. The 'A ÷ B (Ratio)' output on this calculator is exactly that: for a 3:4 ratio, it shows 0.75, meaning for every 1 unit of B there are 0.75 units of A.
Ratio and proportion typically shows up in middle school math curricula, building through applications in scaling, unit rates, and percentage problems. Standard question types include simplifying a ratio, splitting a quantity by a given ratio, and solving for a missing value in a proportion. The step breakdown on this calculator mirrors the GCD-based working most textbooks expect to see shown.
A ratio compares two quantities of the same kind, wins to losses in a season (8:2, simplified to 4:1). A rate compares quantities of different kinds, expressed 'per unit', miles per hour, dollars per pound, gallons per minute. Rates are really ratios where the numerator and denominator carry different units. Fuel efficiency, hourly wage, and interest rate are all rates rather than ratios in the strict sense.
No, both A and B need to be positive numbers for the ratio math to mean anything. A zero denominator makes the ratio undefined, and negative values don't correspond to a real-world proportion in the way this tool is built to handle. If your Scale to Total is zero, both shares will simply come back as zero.
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