Percentage calculator
Calculate a percent of a number, express one number as a percent of another, or find the whole from a known part and percentage.
Ratio calculator: simplify and solve a proportion
Simplify a two-part ratio and, optionally, calculate the matching second amount for a new first amount. Finite decimal inputs are handled exactly, so a ratio such as 1.5 : 2.25 reduces to 2 : 3.
Free to use, with no sign-in. Inputs and results stay in this page and are not sent with the form. Download a result before leaving; this tool does not save your work.
Worked result
1.5 : 2.25 simplifies to 2 : 3; a first amount of 10 matches a second amount of 15.
- Express both finite decimals as exact fractions.
- Clear denominators and divide by the greatest common divisor.
- Keep the same B/A multiplier when scaling.
Scale 1.5 : 2.25 to a first amount of 10
Both amounts must measure comparable quantities in consistent units. Convert the decimal ratio to integers before simplifying.
1.5 : 2.25 = 150 : 225 = 2 : 3
A/B = C/D
D = B × C/A = 2.25 × 10/1.5 = 15
10 : 15 = 2 : 3A part-to-part ratio of 2 : 3 is different from a part-to-whole fraction of 2/3. If there are only two parts, the first is 2/(2 + 3) = 2/5 of the whole.
Simplifying and scaling are different operations
Simplifying a ratio removes a shared scale factor while preserving its relative proportions. Scaling a ratio creates actual amounts at a new size. Neither operation changes the relationship between the two quantities.
Before comparing physical quantities, convert them to consistent units. For example, 1 meter : 50 centimeters is 100 : 50 after conversion, or 2 : 1. This calculator does not infer or convert unit labels.
A : B = (A × L) : (B × L), for any positive L
If A/B = C/D, then D = B × C/A
First share of a two-part total = A/(A + B)Input limits and common mistakes
A and B must be strictly positive. The optional new first amount must be nonnegative. Use finite decimals or scientific notation; units and colon-separated expressions are not accepted in an individual field.
Exact decimal inputs use the same 256-digit and ±300 exponent bounds as the fraction tools. A proportion assumes a linear relationship; real costs, concentrations and physical systems may not remain linear when scaled.
Questions about ratio calculator
What is 1.5 : 2.25 in simplest form?
Multiply both by 100 to get 150 : 225, then divide by 75. The ratio is 2 : 3.
Does 2 : 3 mean two thirds of the total?
No. In a two-part ratio, the total has 2 + 3 = 5 parts. The first quantity is two fifths of the total.
Can I scale a ratio to zero?
A new first amount of zero gives a matching amount of zero. The original ratio still requires positive quantities.
Sources and verification
These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.
- OpenStax: ratios and rates — Ratio interpretation and consistent units.
- OpenStax: proportions — Equivalent ratios and solving for a missing quantity.
Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.
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Further reading
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