What is the formula for Unarmored Movement's bonus?

Question

I'm trying to plug in an equation for a monk's unarmored movement in DiceCloud, so that I don't have to change the bonus value whenever it changes. I had a formula, but lost it. Does anyone know what the formula is?

Answer 1

You can obtain the correct Unarmored Movement for levels when the character has that feature using math.floor((MonkLevel+6)/4)*5. This gives correct unarmored movement for levels 2-20; at level 1 this would give 5 ft. of unarmored movement, but monks don't have the feature at level 1, so you're fine =)

If you're dead-set on inputting the formula at creation and never looking back, just go for if(MonkLevel>1, math.floor((MonkLevel+6)/4)*5, 0).

DiceCloud's helper equations page has other examples, but I find their suggested Unarmored Movement formula overly-wrought, being composed of many logical tests rather than utilizing the fact that the movement rate changes every 4th level.

Answer 2

This is more of an explanation on how to find the formula:

We have here is a set of points where \$x\$ is the level and \$y\$ is the unarmored movement bonus. This gives us the set of points \$S = \{(2,10), \space (6,15), \space (10,20), \space (14, 25), \space (18,30)\}\$.

Fortunately all of these points lie on the line \$y = 1.25x + 7.5\$ which can be rewritten as \$y = \frac{5}{4}(x + 6)\$. Unfortunately just using this equation would get us weird things like having 13.75 bonus movement at level 5 and so we have to remove the parts of the line that are giving us values where we don't want them.

Basically we want to make levels 2-5 identical, levels 6-9 identical, and so forth. These are all intervals of length four so we can use the floor function with division by 4 to get exactly what we need:

\$ y = 5 \times \lfloor {\frac {x+6}{4} } \rfloor \$