Example 1
- Amount: 100
- Ratio: 3 : 2
60 · 40
What does 100 in the ratio 3 : 2 give? 60 and 40.
Ratio Split Calculator
Enter an amount S and two ratio parts a : b. Share 1 = S × a ÷ (a + b), share 2 = S × b ÷ (a + b). 100 in 3 : 2 gives 60 and 40. 90 in 1 : 2 gives 30 and 60. The calculator does not reduce a pair by GCD and does not solve a/b = c/x — it only slices one total into two shares.
Result
Enter the amount and ratio a : b.
Reducing a ratio is on ratio of two numbers. Rule of three: rule of three. GCD: GCD calculator.
How it works
S100
a : b3 : 2
S₁ · S₂60 · 40
The calculator uses the numbers you enter: the amount to split S and two non-negative ratio parts a and b. The model is classical proportional division: treat the whole as a sum of (a + b) equal units; the first side gets a units, the second gets b. Formulas: share 1 = S × a ÷ (a + b), share 2 = S × b ÷ (a + b). For 100 in 3 : 2 the part sum is 5, one unit is 20, so the results are 60 and 40. The shares add back to 100.
Mathematical model: partitioning an amount (or other scalar) in the ratio a : b — proportional allocation. This is not reducing a pair (12 : 8 → 3 : 2); it allocates a ready total under a given ratio. 90 in 1 : 2 yields three units of 30: 30 and 60. 120 in 5 : 1 yields six units of 20: 100 and 20.
The fields are Amount to split, First ratio part, and Second ratio part. Enter 100, 3, and 2, then Calculate. A comma and a period both parse. Parts must be non-negative; both cannot be zero at once. One part equal to zero is allowed: 100 in 1 : 0 gives the whole to the first side.
Reducing 12 : 8 to 3 : 2 lives on the ratio-of-two-numbers page. The rule of three hunts a missing fourth x from a proportion and does not slice one whole. Percentage of a number (15% of 200 = 30) is a different model.
Without the amount or both parts there is no result. 200 in 1 : 1 is 100 and 100. 50 in 2 : 3 is 20 and 30. 120.5 in 2 : 3 is 48.2 and 72.3. Check the 100, 3, and 2 example first.
Formula
For amount S and ratio parts a, b (a ≥ 0, b ≥ 0, a + b > 0):
S₁ = S × a ÷ (a + b)
S₂ = S × b ÷ (a + b)
Unit: u = S ÷ (a + b), then S₁ = a·u and S₂ = b·u. Model: proportional partition (split in ratio a : b).
Theory, proportion, and splitting S
Definition
Dividing an amount S in the ratio a : b (with a ≥ 0, b ≥ 0, a + b > 0) means distributing S into two parts proportional to a and b. The first part is S₁ = S · a / (a + b), the second S₂ = S · b / (a + b). Equivalently: one “ratio unit” has value u = S / (a + b), then S₁ = a · u and S₂ = b · u. By construction S₁ + S₂ = S.
The ratio a : b is a relative weight (part-to-part). Part-of-whole shares are w₁ = a/(a+b) and w₂ = b/(a+b); then S₁ = w₁ · S and S₂ = w₂ · S. When a = 3 and b = 2, w₁ = 3/5 = 0.6 and w₂ = 2/5 = 0.4, so S = 100 yields 60 and 40.
In teaching practice it helps to separate the mathematical formula from floating-point limits: this calculator shows the result of the calculator in the browser (floating-point arithmetic), not a symbolic paper proof. For extreme inputs, check the domain first (nonnegative a, b; a + b ≠ 0), then floating-point range.
Historical and conceptual context
Proportional division is among the oldest practical uses of arithmetic: inheritances, levies, shared costs, mixtures. Euclid’s Elements develops the theory of proportion (Books V–VII): magnitudes are in the same ratio when corresponding multiples preserve inequalities. Modern a : b notation and the weights a/(a+b) became standard in school, bookkeeping, and applied work (recipes, concrete, budget allocation).
Reducing a ratio (shrinking a pair by the GCD — the separate “ratio of two numbers” calculator) differs from allocating a total under a given ratio (this calculator). The rule of three solves a/b = c/x and does not split one sum. The golden ratio φ ≈ 1.618 is the special case (a+b)/a = a/b; the form does not search for φ — you enter your own a, b, and S.
In chemistry a balanced mole ratio (e.g. 2 : 1) supplies the part weights; you scale substance amounts exactly like S₁ and S₂. In descriptive statistics percentage shares are 100 · a/(a+b). This calculator is not a VAT tool and not “percentage of one number.”
In household and business settlements the same formula appears when splitting a bill by room area, allocating a project budget by partner shares, or scaling a paint or concrete recipe. You always need three numbers: the total S and two non-negative weights a and b.
Formal properties
Domain of this calculator: finite S ∈ ℝ, a ≥ 0, b ≥ 0, a + b > 0. Result: S₁, S₂ ∈ ℝ with S₁ + S₂ = S. Homogeneity: kS in the same a : b yields kS₁ and kS₂. Ratio scale: ka : kb for k > 0 yields the same shares as a : b (weights unchanged).
Field order is not writing-identity: 3 : 2 with S = 100 gives 60 and 40, while 2 : 3 gives 40 and 60. When a = b > 0, S₁ = S₂ = S/2. When b = 0 and a > 0, S₁ = S and S₂ = 0. The pair a = b = 0 is excluded (division by zero in a + b).
Check identity: S₁ / a = S₂ / b = u when a > 0 and b > 0. Hence S₁ / S₂ = a / b whenever S₂ ≠ 0.
Full derivation
Step 1. Check that S, a, b are finite, a ≥ 0, b ≥ 0, and a + b > 0.
Step 2. Compute the part sum T = a + b and the unit u = S / T.
Step 3. Set S₁ = a · u = S · a / T and S₂ = b · u = S · b / T.
Step 4. Verify S₁ + S₂ = S. Percentage weights: 100 · a/T and 100 · b/T.
Example 100 in 3 : 2: T = 5, u = 20, S₁ = 60, S₂ = 40. Example 90 in 1 : 2: T = 3, u = 30, S₁ = 30, S₂ = 60.
Special cases
100 in 3 : 2 → 60 and 40; 90 in 1 : 2 → 30 and 60; 50 in 4 : 1 → 40 and 10; 120.5 in 2 : 3 → 48.2 and 72.3; 200 in 1 : 1 → 100 and 100; 120 in 5 : 1 → 100 and 20; 100 in 1 : 0 → 100 and 0.
0 : 0 for any S is a domain error. Negative a or b are rejected. Decimals in S, a, and b are allowed (unlike the ratio-reduction calculator, which requires integers).
Numerical notes
Computation: share1 = (amount * partA) / sum; share2 = (amount * partB) / sum in floating-point arithmetic. The calculator accepts a comma or a period, and grouping spaces, depending on the page language. S₁ + S₂ may drift from S by machine epsilon at extreme magnitudes — the panel shows a check sum.
Very small T relative to |S| yields large |u|; that is a feature of the formula. The tool is educational, not a CAS and not a bookkeeping system with banker’s rounding to cents — displayed rounding comes from formatting, not a separate monetary policy.
Related notions and sources
Related: ratio of two numbers (reducing a : b), GCD, rule of three, percentage of a number, percentage change. For VAT and margin use the percentage calculators on the site.
Sources: Euclid, Elements (proportion); school arithmetic texts (proportional division); MathWorld — Ratio; Wikipedia — Ratio. Educational tool.
How to use
- Enter the amount to split, for example 100.
- Enter the first ratio part, for example 3.
- Enter the second ratio part, for example 2.
- Click Calculate. 100 in 3 : 2 gives 60 and 40. 90 in 1 : 2 gives 30 and 60.
- Check the panel: sum of shares, unit u, and percentage weights. The bar illustrates the split.
- Both parts zero do not run. Reducing 12 : 8 is on ratio of two numbers.
Symbol glossary
100 in 3 : 2 gives 60 and 40. Formula S × a ÷ (a + b) and S × b ÷ (a + b).
- S
- Amount to split. Field “Amount to split”. Example: 100.
- a : b
- Ratio parts. First and second part fields. Example: 3 : 2.
- S₁, S₂
- Shares. S₁ = 60 and S₂ = 40 for 100 in 3 : 2.
- u
- One ratio unit: S ÷ (a + b). For 100 and 3 : 2 that is 20.
- weight %
- 100 · a/(a+b) and 100 · b/(a+b). For 3 : 2 that is 60% and 40%.
Examples
Example 2
- Amount: 90
- Ratio: 1 : 2
30 · 60
What does 90 in the ratio 1 : 2 give? 30 and 60.
Example 3
- Amount: 50
- Ratio: 4 : 1
40 · 10
What does 50 in the ratio 4 : 1 give? 40 and 10.
Example 4
- Amount: 120.5
- Ratio: 2 : 3
48.2 · 72.3
What does 120.5 in the ratio 2 : 3 give? 48.2 and 72.3.
Example 5
- Amount: 200
- Ratio: 1 : 1
100 · 100
What does 200 in the ratio 1 : 1 give? 100 and 100.
Example 6
- Amount: 120
- Ratio: 5 : 1
100 · 20
What does 120 in the ratio 5 : 1 give? 100 and 20.
Example 7
- Amount: 100
- Ratio: 0 : 0
No split
What does 100 in the ratio 0 : 0 give? No split — domain error.
Related calculators
Frequently asked questions
What does this calculator compute?
It splits an amount S in the ratio a : b into S·a/(a+b) and S·b/(a+b). For 100 in 3 : 2 the result is 60 and 40. It does not reduce 12 : 8 and does not run the rule of three.
What is the split formula?
Share 1 = S × a ÷ (a + b). Share 2 = S × b ÷ (a + b). One ratio unit is u = S ÷ (a + b). The shares add back to S.
Must the shares add back to the amount?
Yes. S₁ + S₂ = S by construction. If the displayed sum drifts, check the a and b you entered and floating-point rounding.
Can the ratio parts be zero?
One can be 0; both at once cannot. 100 in 1 : 0 gives the whole to the first side. The pair 0 : 0 is a domain error.
Must the amount be an integer?
No. 120.5 in 2 : 3 gives 48.2 and 72.3. Parts a and b may also be decimals if they stay non-negative and are not both zero.
How is this different from reducing 12 : 8?
There the GCD reduces the pair to 3 : 2. Here you already have a ratio and you split a ready total, e.g. 100 into 60 and 40.
How does the rule of three differ?
The rule of three hunts a fourth number x from a/b = c/x. This page slices one sum S by a : b.
Is 15% of 200 this split?
No. 15% of 200 = 30 lives on the percentage-of-a-number page. Here you enter an amount and two ratio parts.
How do percentage weights work?
The first-part weight is 100 · a/(a+b), the second 100 · b/(a+b). For 3 : 2 that is 60% and 40% — independent of S.
Does the order of a and b change the result?
Yes for which side gets which share: 3 : 2 on 100 is 60 and 40, while 2 : 3 is 40 and 60. The sum is still 100.
Do the currency and unit settings in the page header affect the result?
No. The result depends only on S, a, and b. The currency and unit settings in the page header do not affect this result.
What if a = b?
The shares are equal: half the amount each. 200 in 1 : 1 gives 100 and 100.
How do I divide a number in the ratio a : b?
Enter an amount S and parts a and b (non-negative, not both zero). Share 1 = S × a ÷ (a + b), share 2 = S × b ÷ (a + b). For 100 in 3 : 2 you get 60 and 40; the shares add back to 100.
What is 100 in the ratio 3 : 2?
60 and 40. One ratio unit is 100 ÷ 5 = 20, so three units give 60 and two give 40. That is example 1 on this page.
Does the calculator split into three parts a : b : c?
No. This page slices the amount into exactly two parts a : b. Three-part ratios (e.g. 2 : 3 : 5) are not supported.
Are negative ratio parts allowed?
No. Parts a and b must be ≥ 0. One may be zero (100 in 1 : 0 gives the whole to the first side), but the pair 0 : 0 is a domain error.
How do I check that the split is correct?
Add both shares: they must return to S. For 3 : 2 the percentage weights are 60% and 40% independent of S — a quick proportion check.
Sources
The ratio definition and proportional partition below come from established references.
- Wikipedia — Ratio
- MathWorld — Ratio
- Euclid, Elements (theory of proportion; Books V–VII).
- School arithmetic texts — proportional division / dividing in a given ratio.
Page Updated November 2, 2026.