Ratio Split Calculator Guide

What This Calculator Does

Keep integer ratio simplification, equivalent scaling and missing-proportion solving, and divide a total into two or three ratio shares. Currency mode uses the largest remainder method in integer minor units so the allocated units sum exactly to the total.

When to Use It

Simplify 12:18, generate multiples of 2:3, solve 4:7=x:21, or divide a budget or quantity in ratios such as 2:3 or 1:1:1. Use the fraction calculator for fraction arithmetic and the percentage calculator for percentage changes.

Inputs Explained

Simplify and equivalent modes use integers with absolute values up to 1 billion. The second term cannot be zero. Signed integers are supported, with a negative denominator sign moved to the first term. Scaling uses a whole factor from 1 to 1,000,000, applied to the simplified ratio; reference multiples 1–5 are also shown.

Proportion mode needs three finite numbers and exactly one blank field. Dot/comma decimals and scientific notation are accepted, within ±1 trillion. In the completed a:b=c:d, b and d cannot be zero; the denominator used to solve the missing value must also be nonzero.

Split mode accepts two or three nonnegative integer terms up to 1 billion each, at least one positive, and a total from 0 to 1 trillion. A zero term receives zero. Negative totals and negative split weights are invalid.

Ordinary-number mode returns ideal proportional shares with rounded display. Currency mode explicitly selects 0–3 decimal places for the smallest unit: 0 means whole units, 2 means 0.01 and 3 means 0.001. A total with more decimal digits than the chosen unit is rejected rather than silently rounded. No exchange rates, taxes or automatic currency rules are applied.

Editing clears the previous result; calculate again to update. Existing URL fields restore simplify, equivalent and proportion inputs; new split fields are also preserved in the calculated URL.

How the Calculation Works

Simplify divides both terms by their greatest common divisor. Equivalent mode multiplies the simplified ratio. Proportion solves the missing term through ad=bc.

For total T, terms rᵢ and sum S=Σrᵢ, the ideal share is T×rᵢ/S. Currency mode converts the total into integer minor units M, floors each M×rᵢ/S, then awards unallocated units in descending order of the exact fractional remainders. Ties follow input order. Integer arithmetic avoids binary decimals changing the remainder ranking or losing the balance.

Example

• 12:18 has GCD 6 and simplifies to 2:3; factor 4 gives 8:12.
• In 4:7=x:21, x=12 and both cross products equal 84.
• Total 100 at 2:3 gives 40 and 60.
• Currency total 10.00, two decimals and 1:1:1: each ideal share is 3.333…; floor to 333 minor units each, then award the last unit to the first input. Shares are 3.34, 3.33 and 3.33, totaling 10.00.
• Total 0.01 at 0:1:1 gives 0.00, 0.01 and 0.00. A zero weight never receives a leftover unit.

How to Understand the Result

The result shows the allocated total, individual shares, ratio-term sum and sum check. A one-unit currency difference comes from the deterministic remainder rule. Rounded ordinary-number shares may differ slightly from the displayed total; choose currency mode when the allocated monetary units must add exactly.

Common Mistakes

All-zero split terms; negative split terms; too many total decimal places; a zero second term in simplification; more than one blank proportion field; expecting automatic currency-unit rules.

FAQ

How do I divide a total in a 2:3 ratio?

For total 100 and ratio 2:3, divide by 5 units: the shares are 40 and 60.

Why does one currency share receive an extra cent?

Each share is floored in integer minor units; leftover units go to the largest fractional remainders. Equal remainders use input order.

Are negative ratio terms allowed?

Splitting uses nonnegative terms. Simplify and equivalent modes allow signed integers; the second term cannot be zero.

Notes

Ratio terms are integers up to 1 billion; scales are positive integers up to 1 million. Split totals are 0–1 trillion. Select 0–3 currency decimals explicitly; no currency conversion or live rates.