What this ratio calculator does
A ratio compares quantities by division. Writing 2 : 3 means that for every two equal units in the first part, there are three equal units in the second part. It does not name a unit by itself: two cups to three cups, two people to three people, and two pixels to three pixels can all have the same ratio.
The Ratio Calculator has three separate local calculations. It reduces a two-part ratio to its simplest whole-number form, finds one missing value in an equivalent ratio, and divides a total between two shares. Nothing you enter is sent to a server. It is designed for ordinary positive quantities such as recipe portions, classroom groups, a budget you already chose, or a simple scale sketch.
Ratios are multiplicative relationships, not subtraction. A 2 : 3 split is not “one less”; it is five equal ratio parts in total. The official National Curriculum in England mathematics guidance similarly treats ratio as a way to compare quantities and solve unequal-sharing and proportional problems.
How to simplify a ratio
Use Simplify a ratio when both values are known and measured in the same unit.
- Enter the first and second positive values.
- Read the smallest whole-number ratio and the equivalent fraction.
- Keep the order intact:
2 : 3and3 : 2describe different comparisons.
The calculator turns finite decimals into scaled integers, then divides both values by their greatest common divisor (GCD). For whole numbers this is the familiar rule:
simplified a : b = (a ÷ GCD(a, b)) : (b ÷ GCD(a, b))
For example, 24 : 36 has a GCD of 12, so the simplified ratio is 2 : 3. For decimals, 1.2 : 1.8 is first treated as 12 : 18, which also reduces to 2 : 3. Enter values with no more than ten decimal places; that keeps the browser calculation transparent and avoids implying exactness where a measurement was rounded.
Do not simplify mixed units directly. 2 feet : 36 inches is not 1 : 18; first convert 2 feet to 24 inches with the US unit converter, then simplify 24 : 36 to 2 : 3.
How equivalent ratios work
Equivalent ratios preserve the same multiplier. If a : b = c : d, then cross-products match:
a × d = b × c
Leave exactly one box blank in the equivalent-ratio panel. The tool solves it with division. With 2 : 3 = 10 : ?, the first number was multiplied by 5, so the second number must be 3 × 5 = 15. The result is 2 : 3 = 10 : 15.
This works only when the relationship is genuinely proportional. If a delivery fee is added after a per-item price, or a tax threshold changes the rate, a single ratio may not describe the whole situation. Use the percentage calculator when the question is specifically “what percent of a total?” rather than “what two quantities are in the same proportion?”
How to split a total by ratio
To distribute a total T in an a : b ratio, first count the ratio parts, then assign the same fraction of the total to each side:
total parts = a + b
first share = T × a ÷ (a + b)
second share = T × b ÷ (a + b)
For a 500-unit total split 2 : 3, there are five parts. One part is 500 ÷ 5 = 100, so the shares are 200 and 300. The panel also shows 40% and 60%, because 2 ÷ 5 = 40% and 3 ÷ 5 = 60%.
The result can contain decimals. That is mathematically correct, but real objects may be indivisible. If you are splitting five whole tickets, a 2:3 split is exact; if you are splitting seven whole tickets, you must decide how to round before assigning the final ticket. The calculator intentionally does not choose that policy for you.
Examples and common uses
Scale a recipe
Suppose a dressing uses 2 tablespoons of oil for every 3 tablespoons of vinegar. The ratio is 2 : 3. To make 10 tablespoons total, use the sharing panel: 4 tablespoons of oil and 6 tablespoons of vinegar. If your original recipe gives one ingredient and you need the other, enter the known three values in the equivalent-ratio panel.
Compare two groups
If 18 people choose option A and 27 choose option B, simplify 18 : 27 to 2 : 3. This describes the relative group sizes, not a percentage of a larger population. For the percentage of the 45 people in each group, use the percentage calculator.
Check an aspect relationship
An image that is 1920 by 1080 pixels reduces from 1920 : 1080 to 16 : 9. The ratio states the shape. It does not resize, crop, or inspect an image; use your graphics software for those tasks.
Divide a budget already approved
A 900-unit project allocation split 1:2 gives 300 and 600. This is arithmetic only. It does not account for fees, taxes, contracts, eligibility, currency conversion, or a fairness rule. For price changes and sale reductions, the discount calculator is the more specific tool.
Limits and accuracy notes
This page accepts two positive ratio terms. It does not solve three-part ratios, inverse proportions, optimization problems, or formulas with fixed additions. It also cannot determine whether an input is a sensible real-world measurement. Confirm units before reducing or comparing values.
For money, the displayed result may have more than two decimal places. Decide independently whether to round to cents and how to handle any leftover cent. For regulated allocation, tax, payroll, legal ownership, medical dosing, or safety-critical measurements, use the applicable official rules and a qualified professional; a general ratio calculation is not a decision or compliance tool.