Question

I need to compute the steps between a start and end in a range for the purpose of sizing fonts.

Given:

Start Value: 14.0,
End Value: 250.0,
Steps: 28

Resulting Values: 14.0, 15.5, 17.1, 18.9, ... 204.9, 226.3, 250.0

I calculated each value by adding 10.45% to the previous value (based on trial and error), but how do I calculate this percentage?
Guessing there is some compounding interest type function that could be used here.
A formula or pseudo code is fine.

Ultimately, this will be a C#.

Answer 1

EndValue = StartValue * ( ( 1 + Percentage ) ^ NumberOfSteps )

is the basic formula you will need.

If you know the NumberOfSteps and you want the Percentage, a bit of algebra will get you the formula (pseudocode, ^ is the exponent operator):

EndValue / StartValue = ( 1 + Percentage ) ^ NumberOfSteps
(EndValue / StartValue) ^ (1 / NumberOfSteps) = 1 + Percentage
Percentage = ( (EndValue / StartValue) ^ (1 / NumberOfSteps) ) - 1

If you know Percentage and you want NumberOfSteps, you’re better off with a loop

int NumberOfSteps = 0;
for(double i = StartValue; i < EndValue; i *= (1 + Percentage))
{
    ++NumberOfSteps;
}