Calculate ladder angle, vertical rise, base distance, or working length from a supported pair of known values. Select units for each input; the calculator converts meters, feet, inches, centimeters, degrees, and radians automatically.

Right-triangle geometry only; results do not establish a safe ladder setup. Height is vertical rise, not ladder length. Working length runs from the foot to top support. Follow the ladder manufacturer and applicable safety rules.

Ladder Angle Formula

The ladder angle is the angle between the ladder and the ground. When a ladder leans against a wall, it forms a right triangle, so the angle can be found with basic trigonometry from the ladder length, the base distance, and the vertical rise.

θ = tan⁻¹((H) / (B))

Use that form when H is the vertical rise and B is the horizontal base distance from the wall to the foot of the ladder.

The calculator distinguishes vertical rise H from working ladder length L. These equivalent relationships cover its other input pairs:

Known values Formula
Vertical rise and base distance
θ = tan⁻¹((H) / (B))
Ladder length and angle
B = Lcos(θ)
Ladder length and angle
H = Lsin(θ)
Ladder length and base distance
θ = cos⁻¹((B) / (L))
Ladder length and vertical rise
θ = sin⁻¹((H) / (L))
Any right-triangle ladder setup
L = √(H² + B²)

Variable Definitions

  • θ = ladder angle measured from the ground
  • L = working ladder length from the foot to the top support point, excluding any extension above that support
  • H = vertical rise up the wall or support point
  • B = base distance from the wall to the foot of the ladder

How to Use the Ladder Angle Calculator

  1. Select the pair you know, then enter those two values.
  2. Select the correct unit for each length; mixed units are converted automatically.
  3. Select degrees or radians for the angle input.
  4. Calculate the missing value and verify the setup against your intended reach and base spacing.

This calculator is most helpful in two common situations:

  • You know the rise and the base and want the ladder angle.
  • You know the ladder length and target angle and want the correct base distance.

4:1 Placement Rule

For non-self-supporting ladders covered by OSHA construction rules, the horizontal base distance is approximately one-quarter of the working length from the foot to the top support. Follow the applicable rules and manufacturer guidance for your ladder.

B ≈ (L) / (4)

With an exact working-length-to-base ratio of 4:1, the angle is:

θ = cos⁻¹((1) / (4)) ≈ 75.52^°

NIOSH describes a setup angle around 75.5°. A geometric rise-to-base ratio of 4:1 instead gives about 75.96°; it is not the same definition as OSHA’s working-length rule. These calculations alone do not establish a safe or compliant setup. See OSHA 1926.1053(b)(5)(i) and NIOSH’s ladder angle guidance. Smaller angles make the ladder flatter and push the base farther away; larger angles make it steeper and bring the base closer.

Examples

If the working ladder length is 16 ft, the working-length 4:1 rule gives:

B ≈ (16) / (4) = 4

The horizontal base distance is about 4 ft, giving a vertical rise of about 15.49 ft in the right-triangle model.

If the working ladder length is 20 ft and the angle is 75°:

B = 20cos(75^°) ≈ 5.18
H = 20sin(75^°) ≈ 19.32

So the ladder reaches about 19.32 ft vertically, with the base about 5.18 ft from the wall.

Degrees and Radians

If the calculator is set to radians, enter the angle in radians instead of degrees.

75^° ≈ 1.309 rad

Common Input Mistakes

  • Confusing ladder length with vertical rise.
  • Measuring the angle from the wall instead of from the ground.
  • Selecting the wrong unit for a length. Mixed units are supported when each unit selector is correct.
  • Entering degrees while the calculator is set to radians, or the reverse.
  • Measuring the base distance diagonally instead of straight along the ground.

Practical Notes

  • The wall, ground, and ladder should be treated as a right-triangle model for these formulas to apply cleanly.
  • For a fixed ladder length, increasing the angle increases the vertical reach and decreases the base distance.
  • For a fixed rise, increasing the base distance decreases the angle.
  • If you are setting up a ladder in the real world, always check the surface, ladder condition, and manufacturer guidance in addition to the math.