Figure

Math and relationships

Tangent

Relate rise, horizontal run, and the angle of a right triangle.

Tangent is the ratio of opposite side to adjacent side in a right triangle. With an angle measured from horizontal, that is rise ÷ run. The sloping length is a different side and cannot replace the horizontal run.

Find rise from run and angle

Find how far a slope rises over a known horizontal distance.

What tangent gives you

tan gives rise ÷ run for an angle. Multiply that ratio by the run to get the rise.

Right triangle: a 45 degree slope has a 6 foot horizontal run. Tangent times run gives a 6 foot vertical rise.6 ftrise45°
Schematic, not to scale.

Try it · 6 ft run at 45°

Enter the angle without units. Use 2nd if Feet is above its key.

  1. Start fresh

    Press Clear entry, then Clear entry, then Select length units.

  2. Tangent of the angle

    Press 45, then Tangent, then Multiply.

  3. Multiply by horizontal run

    Press 6, then feet, then Equals.
  1. Vertical rise6 feet 0 inches

Also useful for

Roof slopes, ramp layouts, angled brackets and pipe or duct offsets when you know the angle and horizontal run.

Remember

Measure the angle from horizontal. Run is the horizontal distance, not the slant. A 45° slope has equal rise and run.

Tangent of 75°

Enter the angle in degrees without a length unit.

Start a new calculation

  1. Press Clear entry, then Clear entry.

Calculate

  1. Angle in degrees

    Press 75, then Tangent.
  1. Example result3.732051

Keep the guide beside your calculation.

These examples are built into Figure. Open Help while you calculate, then return to the same guide and reading position.

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