How this instrument works
Inverse tangent (arctangent) answers the question 'what angle has this tangent value?' — given a rise-over-run slope ratio, arctangent returns the angle that slope represents. This page frames that calculation as a RAMP or GRADE problem: how steeply an incline climbs, given how much it rises over a given horizontal run.
This uses the same rise/run language as this site's Rise Over Run calculator, but instead of stopping at the slope ratio itself, this page carries that ratio one step further into the actual incline angle — the number a carpenter, road engineer, or hiker would actually want when comparing how steep two different slopes really are.
This is the identical mathematical operation as this site's more abstract Inverse Tangent (tan⁻¹) button-notation page — the underlying arctangent function doesn't change, only the labeled fields and the practical framing around it.
- Enter the vertical rise into the Rise field.
- Enter the horizontal run into the Run field.
- Read Angle of incline: the slope converted directly into an angle.
- Try an equal rise and run to see the incline settle at exactly 45°.
Worked example — rise 3, run 4
A ramp rising 3 units over a run of 4 units climbs at an angle of atan(3⁄4)≈36.87° — inverse tangent converting that slope ratio directly into a real incline angle.
A rise of 0 over any run gives an incline angle of exactly 0° — a perfectly flat, level surface. An equal rise and run (10 and 10) gives an incline angle of exactly 45° — a slope of 1, splitting the angle evenly between horizontal and vertical.
Questions
What does inverse tangent find here?
The angle a ramp, road, or hillside climbs at, given its rise-over-run slope ratio — arctangent converts that plain ratio directly into a real incline angle.
How is this different from this site's Rise Over Run calculator?
That page reports the slope ratio itself; this page carries that same ratio one further step, through inverse tangent, into an actual incline angle — a more intuitive figure for comparing how steep two different slopes really are.
How is this different from this site's plain Inverse Tangent (tan⁻¹) page?
Both compute the identical arctangent operation; this page frames it specifically as a ramp/grade slope-to-angle question with labeled rise and run fields, while the other page works directly with a bare ratio using calculator-button notation.
What incline angle does a slope of 1 give?
Exactly 45° — whenever the rise and run are equal, the incline splits evenly between horizontal and vertical, landing at the midpoint angle.
What happens as the run shrinks toward 0?
The incline angle climbs toward 90° — a run approaching zero with any positive rise describes an increasingly vertical, cliff-like slope.