The dimensionless slope s = rise/run is the common core. Percent is 100s, per mille is 1000s, angle is arctan(s), and a 1:N ratio has |s| = 1/N.
Percent and per mille are linear
A slope of 0.05 is exactly 5% and 50‰. Multiplying by 100 or 1000 does not introduce approximation.
Angle uses trigonometry
Because angle = arctan(s), 100% means arctan(1) = 45°. Most other angle results are irrational and must be rounded.
State the ratio direction
SlopeCalc defines 1:N as one vertical unit per N horizontal units. Other documents may reverse or describe ratios differently, so preserve the definition with the number.
Compare representations through the shared slope
When two documents use different notation, first convert each value to rise divided by horizontal run. Comparing that common dimensionless number avoids treating percent, degrees, per mille, and 1:N as if their printed values had the same scale.