What This Tool Does
What is a Proportion Calculator? Use it to solve one unknown value in a direct or inverse proportion. It accepts three known values and shows the rearranged formula, substitution steps, assumptions, and result representations.
Pick a proportion type and which of the four values (a, b, c, or d) is unknown, then enter the other three. A direct proportion solves a/b = c/d; an inverse proportion solves a × b = c × d. The calculator rearranges the formula for your unknown, substitutes your values, and shows the exact result.
Direct vs. Inverse Proportions
A direct proportion means two ratios are equal: a/b = c/d. As one ratio's numerator grows, so does the matching value, proportionally - for example, distance traveled at a constant speed grows directly with time. The calculator solves for any one of the four values by cross-multiplication, e.g. solving for d gives d = (b × c) / a.
An inverse proportion means two values multiply to the same product: a × b = c × d. As one value grows, its paired value shrinks so the product stays constant - for example, the time to finish a job shrinks as the number of workers grows, for a fixed amount of work. The calculator solves for any one of the four values, e.g. solving for d gives d = (a × b) / c.
Enter Values and Optional Unit Labels
Choose Solve for a, Solve for b, Solve for c, or Solve for d. Changing the unknown clears and disables that input. Enter whole numbers such as 7, decimals such as 2.5, or fractions such as 3/4 in the other three fields. Values must be zero or positive.
Unit for a and b and Unit for c and d are optional labels. They appear beside the solved value and in the equation and copyable output. They do not convert units; enter each pair in compatible units.
Results and Decimal Display
The calculator uses exact fraction arithmetic with arbitrary-precision integers. The fraction is the exact result; the mixed number and decimal are additional representations. Terminating or detected repeating decimals may use notation such as 0.(3). If a repeating cycle is longer than the display window, the decimal is abbreviated with an ellipsis.
How to Use the Proportion Calculator
- Choose the type: direct (a/b = c/d) or inverse (a × b = c × d).
- Choose Solve for a, Solve for b, Solve for c, or Solve for d.
- Enter the three known values.
- Optionally enter the two unit labels.
- Click Calculate, then review Result, Steps, and Assumptions.
- Use Copy result or Download result (.txt) to save the working.
Errors and Input Limits
If Calculate shows an error, check that all three known fields are filled with supported numbers, the selected unknown is blank, values are not negative, and fraction denominators are not zero. Some rearrangements also fail when the divisor is zero. Changing the proportion type or unknown hides the previous result until you calculate again.
Privacy and Scope
The calculator parses and calculates your proportion values locally in the browser; its calculator workflow does not submit those values to a server. It does not fetch outside data or provide certified engineering, financial, or medical advice.
Frequently Asked Questions
What is the difference between a direct and an inverse proportion?
In a direct proportion, a/b = c/d - as one ratio increases, the matching value increases proportionally, and you solve it by cross-multiplying. In an inverse proportion, a × b = c × d - as one value increases, the other decreases so their product stays constant. Pick the type that matches your situation, enter the three known values, and the calculator solves the fourth.
What number formats can I enter?
Whole numbers (7), decimals (2.5), and simple fractions (3/4). Proportion terms must be zero or positive, since a negative term is not meaningful in a ratio.
Does the calculator convert between units?
No. The unit fields are optional labels only, carried through to the result text so you can keep track of what each pair of values represents (e.g. km and hours). The calculator does not infer or convert between unit systems - enter all values for each pair already in the same unit.
Does the calculator round results?
The fraction is the exact result and is not rounded. A decimal equivalent is shown alongside. Terminating or detected repeating decimals may use notation like 0.(3); longer repeating cycles can be abbreviated with an ellipsis.
What should I check if Calculate shows an error?
Check that all three known fields contain a whole number, decimal, or fraction such as 3/4, that no value is negative, and that fraction denominators are not zero. Leave the selected unknown blank. Some rearrangements also fail when the value used as a divisor is zero.
Is this certified or professional advice?
No. This is a general-purpose arithmetic tool for solving proportions. It performs deterministic math on the exact values you enter and does not fetch outside data or infer professional, engineering, financial, or medical assumptions on your behalf.