Calculate the increase ratio and percent increase from an initial and final value, or find the change, initial or final value from a known ratio.

Use the same unit for all values. Negative values are allowed.

Optional settings

Increase Ratio Formula

The following formula is used to calculate the Increase Ratio. 

IR = TI / IV

  • Where IR is the Increase Ratio
  • IV is the initial value 
  • TI is the total increase (final value − initial value)

Divide total change by the nonzero initial value. Percent change equals the decimal ratio ×100. The final/initial multiplier equals1 + ratio. Negative initial values retain their signed denominator and need care in interpretation. To reverse the model, choose Initial value (change ÷ ratio), Total change (initial × ratio), or Final value (initial × (1 + ratio)). Zero ratio and zero change have no unique initial value.

Increase a value in a given ratio

For a ratio written as new:original = a:b, the new value is original × a ÷ b. The change is new − original, and percent change is (a/b − 1) × 100. For example, increasing 250 in the ratio 7:5 gives 250 × 7 ÷ 5 = 350, an increase of 100 or 40%.

Select Scale a value by a:b for this calculation. Both terms and the value must be positive. A larger first term increases the value; a smaller first term decreases it. This new:original ratio differs from the change/initial increase ratio used in the other modes.

How to Calculate Increase Ratio?

The following example problems outline how to calculate the Increase Ratio.

Example Problem #1:

  1. First, determine the initial value.
    • The initial value is given as 5.
  2. Next, determine the final value.
    • The final value is provided as 15.
  3. Finally, calculate the total increase (TI = final − initial), then compute the Increase Ratio: IR = TI / IV (multiply by 100 to express it as a percent).

IR = (FV − IV) / IV

The values given above are inserted into the equation below and the solution is calculated:

TI = 15 − 5 = 10; IR = 10 / 5 = 2.0000 (decimal) = 200.00%

Example Problem #2: 

For this problem, the variables required are provided below:

initial value = 6

final value = 8

Test your knowledge using the equation and check your answer with the calculator above.

IR = (FV − IV) / IV = (8 − 6) / 6 = ?