Proportion Calculator: Direct and Inverse
By Hesaplayıcı
The proportion calculator finds the unknown x in the proportion a : b = c : x. Enter the three known values and choose direct or inverse proportion. In a direct proportion both quantities grow together; in an inverse one, one grows as the other shrinks. You get x, the constant of proportionality and every step.
Worked example: If 3 pens cost 12, what do 5 pens cost? (direct)
x (the unknown)
20
- Constant of proportionality (k)
- 4
Step by step
Constant of proportionality (k)
k = b / a
k = 12 / 3 = 4
x (the unknown)
x = b × c / a
x = 12 × 5 / 3 = 20
How to use
- Enter a, a known value of the first quantity, for example a number of pens.
- Enter b, the value of the second quantity that goes with a, for example the price of those pens.
- Enter c, the new value of the first quantity.
- Choose Direct proportion or Inverse proportion and press Calculate.
Formula
- Direct proportion:
a / b = c / x, sox = b × c / a. The constant isk = b / a. - Inverse proportion:
a × b = c × x, sox = a × b / c. The constant isk = a × b.
a and c are two values of the first quantity. b and x are the matching values of the second quantity. k is the amount per unit of the first quantity in a direct proportion, and the fixed product of the two quantities in an inverse one. Cross multiplication gives the same result: a × x = b × c.
Worked example
The worked example on this page finds the price of 5 pens when the price of 3 pens is known, as a direct proportion. The first step gives the constant, the price of one pen; the second gives x.
Limits
The calculator solves a simple proportion of two quantities, not a compound proportion of three or more. The divisor cannot be zero: a in a direct proportion, c in an inverse one. There are no units: x is in the unit of b. The result is not rounded; the page may shorten numbers.
Frequently Asked Questions
What is a direct proportion?
Two quantities are in direct proportion when one grows or shrinks by the same factor as the other. The ratio of matching values stays the same.
What is an inverse proportion?
Two quantities are in inverse proportion when one grows by the same factor as the other shrinks, so the product of matching values stays the same. For example, if 4 people paint a fence in 3 hours, 6 people paint it in 2 hours.
How do you solve a proportion by cross multiplication?
In a / b = c / x, multiply across: a × x = b × c. Then divide by a to get x = b × c / a.
Can a proportion contain zero?
The divisor cannot be zero, because division by zero is undefined. If a is zero in a direct proportion, or c in an inverse one, the calculator returns an error.
Calculation rules
- In a direct proportion both quantities grow or shrink together: a / b = c / x, so x = b × c / a and the constant is k = b / a.
- In an inverse proportion one grows as the other shrinks by the same factor: a × b = c × x, so x = a × b / c and the constant is k = a × b.
- The divisor cannot be zero: a for a direct proportion, c for an inverse one.
- The result is not rounded; the page may shorten numbers.