Angle Cut Calculator
The Angle Cut Calculator finds the cut angle for a sloped piece from its rise and run, using the inverse tangent. It also returns the complementary angle. The formula used is: cut angle = arctan(rise ÷ run).
Formula
Cut Angle = arctan(Rise ÷ Run)
- The Angle Cut Calculator updates instantly when you change the rise or run.
- Formula: cut angle = arctan(rise ÷ run)
- Input definitions: • Rise: the vertical change of the slope • Run: the horizontal distance over that rise
- The complementary angle (90° − cut angle) is the matching angle for the opposite face of the cut.
- Rise and run must share the same unit; the resulting angle is the same regardless of the unit used.
- Practical tip: for a 4-in-12 roof pitch, enter rise 4 and run 12 to get the rafter cut angle.
Example Calculation
Inputs
- Rise: 4
- Run: 12
A 4-in-12 slope gives cut angle = arctan(4 ÷ 12) ≈ 18.43°, with a complementary angle of 90° − 18.43° = 71.57°.
Frequently asked questions
How is the cut angle found?
Take the inverse tangent of the rise divided by the run: cut angle = arctan(rise ÷ run).
What is the complementary angle for?
It is 90° minus the cut angle — the angle you set on the opposite face or the matching piece so the two parts fit.
What units should I enter?
Use any length unit for rise and run as long as both match. The angle result is unit-independent.
Can I use this for roof pitch?
Yes. Enter the pitch as rise over run (e.g. 4 and 12) to get the rafter or fascia cut angle.
How accurate are the results?
The angle is computed exactly from rise and run and rounded only for display.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.