Ratio Calculator - Simplify & Scale Ratios

Value A3

Value B4

Scale to Total700

A ÷ B (Ratio)

0.75

A as % of Total

42.86%

B as % of Total

57.14%

A's Share (of Total)

300

B's Share (of Total)

400

What is a Ratio?

A Ratio Calculator simplifies any ratio A:B to its lowest terms, computes the percentage share of each term in the combined total, and splits any given total in the exact ratio specified. These three operations together cover every practical ratio problem — from verifying a recipe scale-up to splitting a business investment or checking a map scale.

A ratio is the comparison of two quantities by division: the ratio A:B tells you how A and B relate in size. Unlike fractions, ratios emphasise the relative proportion of two distinct quantities rather than one being a part of another. A partnership that splits profits in a 3:4 ratio means the first partner receives 3 parts for every 4 parts the second partner receives — for a combined pool of ₹7 lakh, that translates to ₹3 lakh and ₹4 lakh.

The fundamental operation that unlocks all ratio problems is the GCD — Greatest Common Divisor. Dividing both terms of a ratio by their GCD gives the simplest form: 12:18 simplifies to 2:3 (GCD = 6), and 1.5:2.5 simplifies to 3:5 (multiply by 2, GCD of 30 and 50 = 10). The step breakdown on this calculator shows this simplification explicitly, making it directly usable for CBSE/ICSE homework where the working must be shown.

The Scale To Total field is the most practically useful feature: enter the total amount you want to distribute (say, ₹7,00,000 for a partnership, or 100 for converting to percentages) and the calculator immediately returns each party's share. This covers the most common ratio application in Indian finance — splitting profits, losses, inheritance, and joint investments.

For comparisons between two datasets, the Percentage Change Calculator expresses a ratio as relative change, while this calculator expresses it as a fixed proportion.

How to use this Ratio calculator

Enter Value A — the first term of the ratio. Can be any positive number, including decimals. For a 3:4 split, enter 3. For a financial ratio like P/E of 24.5, enter 24.5.
Enter Value B — the second term. Must also be positive. The ratio A:B compares A to B directly; the order matters (3:4 and 4:3 are different ratios).
Enter Scale To Total — the total quantity you want to split in this ratio. Default is 700 (so a 3:4 split gives 300 and 400 for easy verification). For partnership splits, enter the profit or loss amount. For percentage conversion, enter 100 (gives direct percentage shares). For a 1,000 ml solution split, enter 1000.
Read A ÷ B and the percentage splits — the decimal ratio and percentage-of-total outputs give a complete picture of the proportion.
Expand the step breakdown — the GCD computation and simplified ratio are shown explicitly. For 12:16, you'll see GCD = 4 → simplified ratio = 3:4. This is the working required in school examinations.

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 Scale To Total T):
(A ÷ (A + B)) × T

B's Share (of Scale To Total T):
(B ÷ (A + B)) × T

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

GCD for decimal inputs (up to 2 decimal places):
GCD(A, B) is computed on integers A × 100 and B × 100, then the simplified integers are divided back by 100 if needed — so 1.5:2.5 → GCD(150, 250) = 50 → 3:5

Worked example — A = 5, B = 8, Scale To Total = ₹2,60,000:

GCD(5, 8) = 1 → already in simplest form 5:8A as % of Total = (5 ÷ 13) × 100 = 38.46%B as % of Total = (8 ÷ 13) × 100 = 61.54%A's Share = 38.46% × 2,60,000 = ₹1,00,000B's Share = 61.54% × 2,60,000 = ₹1,60,000

Worked example — simplification — A = 24, B = 36, Scale To Total = 100:

GCD(24, 36) = 12 → Simplified ratio = 2:3A as % of Total = (24 ÷ 60) × 100 = 40%B as % of Total = (36 ÷ 60) × 100 = 60%A's Share of 100 = 40 | B's Share = 60

Assumptions and limitations:
- Both A and B must be positive. Zero or negative ratios are not meaningful for proportion calculations
- Scale To Total of 0 gives shares of 0 — enter a positive value to see shares
- All outputs are rounded to 2–4 decimal places depending on the output type; the Average Calculator can be used to compute the mean of a series of ratios

Frequently Asked Questions

What is a ratio and how is it different from a fraction?

A ratio expresses the relative size of two or more quantities and is written as A:B. It tells you how many times one quantity contains the other or how they compare in size — for example, 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 representing A divided by B, always expressing A as a part of B. While A:B can be converted to the fraction A/B (giving the decimal ratio), the ratio notation emphasises comparison between distinct quantities rather than a part-of-a-whole relationship.

How do I simplify a ratio?

To simplify a ratio A:B, divide both terms by their Greatest Common Divisor (GCD). GCD(12, 16) = 4, so 12:16 simplifies to 3:4. For decimal ratios like 1.5:2.5, multiply both by 10 to get 15:25, then divide by GCD(15,25) = 5, giving 3:5. A simplified ratio has no common factor between its terms — it is in its lowest terms. The Step Breakdown on this calculator shows the GCD and the simplified ratio for every pair of inputs.

How do I split a total amount in a given ratio?

To divide a total T in ratio A:B, first find each party's share of the total: A's share = (A ÷ (A+B)) × T; B's share = (B ÷ (A+B)) × T. For example, splitting ₹7,00,000 in a 3:4 partnership: A's share = (3 ÷ 7) × 7,00,000 = ₹3,00,000; B's share = (4 ÷ 7) × 7,00,000 = ₹4,00,000. Enter A, B, and T (in the 'Scale To Total' field) on this calculator to get both shares instantly.

What is the difference between ratio and proportion?

A ratio is the comparison of two quantities (A:B). A proportion is a statement that two ratios are equal: A:B = C:D, or equivalently A/B = C/D. Proportion allows you to solve for a missing value when three of the four quantities are known: if 3:4 = C:20, then C = 3 × 20 ÷ 4 = 15. The cross-multiplication rule for solving proportions — A × D = B × C — is a core technique in CBSE/ICSE mathematics. Ratios describe a relationship; proportions use that relationship to find unknown values.

How do I find a missing value in the proportion A:B = C:D?

Use cross-multiplication: A × D = B × C. If 3:4 = C:20, then 3 × 20 = 4 × C, so C = 60 ÷ 4 = 15. If A:5 = 6:15, then 15A = 30, A = 2. For direct proportion (both quantities change in the same direction), the formula is straightforward. For inverse proportion (one increases as the other decreases), flip one ratio: A:B = D:C. This calculator computes ratio decimals and percentage splits — for the missing-value proportion problem, the step breakdown shows the working for the scaled shares.

How do I convert a ratio to a percentage?

In ratio A:B, A's percentage of the combined total (A+B) is: (A ÷ (A+B)) × 100. For ratio 3:7 with total 10: A = (3÷10) × 100 = 30%; B = (7÷10) × 100 = 70%. If the ratio represents A relative to B alone (not the total), the percentage is: (A÷B) × 100. For 3:4, A is (3÷4) × 100 = 75% of B. This calculator shows both — 'A ÷ B (Ratio)' gives the decimal form of A relative to B, while 'A as % of Total' and 'B as % of Total' give the split of the combined total.

How are ratios used in financial statements and business analysis?

Financial ratios are fundamental analytical tools: the current ratio (current assets:current liabilities) measures liquidity; the debt-to-equity ratio measures leverage; the P/E ratio (price per share:earnings per share) measures valuation. In Indian business contexts, the gross profit ratio, inventory turnover ratio, and return on equity are standard KPIs. A ratio of 2:1 for current assets to liabilities means the business has twice as many short-term assets as liabilities — generally considered financially healthy.

Can a ratio have decimal or fractional values?

Yes — ratios can have any real positive values. A ratio of 1.5:2.5 is valid and simplifies to 3:5 (multiply both by 2). Ratios with decimals are common in financial analysis (e.g., P/E ratio of 24.6:1) and in mixing problems (2.5 litres of solution A to 3.75 litres of solution B = 2:3 simplified). This calculator handles decimal inputs and uses a 2-decimal-precision GCD algorithm to simplify them correctly in the step breakdown.

What is a unit ratio and how is it used?

A unit ratio is a ratio of the form 1:N or N:1, where one term has been reduced to 1. It is the most intuitive format for comparison: a scale drawing at 1:100 means 1 cm on paper represents 100 cm in reality. The 'A ÷ B (Ratio)' output on this calculator is the decimal form of the unit ratio A:B expressed as A/B — for ratio 3:4, it is 0.75 (i.e., for every 1 unit of B, there are 0.75 units of A). Unit ratios are also used in map scales, model dimensions, and gear ratios.

How are ratios used in CBSE/ICSE Class 6–10 mathematics?

Ratios are introduced in CBSE Class 6 (Chapter: Ratio and Proportion) and developed through Class 8 with applications in direct and inverse proportion, percentage, and unitary method. ICSE covers ratios in the same progression. Standard problem types include: simplifying ratios, dividing a quantity in a given ratio, finding the ratio between two quantities, and solving proportion problems. The step breakdown on this calculator shows GCD-based simplification in a format consistent with school examination working.

What is the difference between ratio and rate?

A ratio compares two quantities of the same kind — for example, wins to losses in a cricket series (8:2 = 4:1). A rate compares two quantities of different kinds, expressed as 'per unit': km per hour, rupees per kg, litres per minute. Rates are ratios with different units in numerator and denominator. Speed, price per unit, and interest rate are all rates. When someone says 'the ratio of petrol to diesel cars in India', they mean the count ratio — same unit. When they say '18 km per litre', that is a rate — different units.