Calculate a missing value in an inverse proportion problem. Enter three known values to find the answer instantly, with a clear formula and step-by-step explanation.
Enter three values from your problem.
Inverse proportion formula
Multiply the first and second values, then divide by the third value.
The original quantity.
The corresponding original result.
The new quantity that changes inversely.
Original pair
4:12
New pair
6:8
In inverse proportion, the product of the paired quantities remains constant.
Your missing value updates automatically.
Calculated value (X)
8
If 4 corresponds to 12, then 6 corresponds to 8 in an inverse proportion.
Write the formula
X = (A × B) ÷ C
Substitute the values
X = (4 × 12) ÷ 6
Multiply A by B
X = 48 ÷ 6
Divide by C
X = 8
The inverse rule of three is a method for finding an unknown value when two quantities change in opposite directions. When one quantity increases, the other decreases in a way that keeps their product constant.
For example, if more equally productive workers are assigned to the same fixed job, fewer days are needed to finish it. This method can also be useful for constant-distance speed problems and other inverse proportion calculations.
If A corresponds to B and C is the new quantity, the missing value is X = (A × B) ÷ C. This formula applies when the quantities are inversely proportional.
Use it when increasing one quantity causes the other to decrease proportionally. A common example is the time needed for a fixed job when the number of equally productive workers increases.
In direct proportion, both quantities move in the same direction. In inverse proportion, one increases while the other decreases, assuming a constant product.
Yes. You can enter decimal values for measurements, speed, time, and other numerical quantities. The calculator updates the answer automatically.
Yes, the second value can be zero, producing a result of zero. The first and third values must be greater than zero for this formula to work.