Ladder angle calculator
- Rule: base out from the wall ≈ 1/4 of the working length (the 4:1 rule), about 75.5° from the ground
- Working length = height of the top support ÷ 0.968 (that's √15 ÷ 4)
- Working length: 12 ÷ 0.9682 = 12.39 ft
- Base distance: 12.39 ÷ 4 = 3.1 ft out from the top support
- Rails must extend 3 ft above the landing. Along the tilted rails that's 3 ÷ 0.9682 = 3.1 ft
- Ladder length needed: 12.39 + 3.1 = 15.49 ft
- Answer: at least 15.49 ft of ladder, foot set 3.1 ft out
The starting value is only an example. Working length is measured along the ladder from the foot to the top support.
Formula and sources
- Base distance = working length ÷ 4 (about 75.5° from the ground)
- Working length = height ÷ 0.9682; add 3 ÷ 0.9682 ≈ 3.1 ft of rail for the 3 ft extension
Example: a 12 ft landing needs a working length of 12 ÷ 0.9682 = 12.39 ft, the foot set 3.1 ft out, and about 15.49 ft of ladder once the 3 ft extension is added.
The formula comes from
29 CFR 1926.1053(b)(5)(i)(opens ecfr.gov in a new tab)“Non-self-supporting ladders shall be used at an angle such that the horizontal distance from the top support to the foot of the ladder is approximately one-quarter of the working length of the ladder (the distance along the ladder between the foot and the top support).”
The formula comes from
29 CFR 1926.1053(b)(1)(opens ecfr.gov in a new tab)“When portable ladders are used for access to an upper landing surface, the ladder side rails shall extend at least 3 feet (.9 m) above the upper landing surface to which the ladder is used to gain access; or, when such an extension is not possible because of the ladder's length, then the ladder shall be secured at its top to a rigid support that will not deflect, and a grasping device, such as a grabrail, shall be provided to assist employees in mounting and dismounting the ladder.”
Formulas and calculators on the BCSP exams
- BCSP gives you no formula sheet, and you can't bring one.
- When a question needs a formula, the formula is written into the question, unless the question is testing whether you know that formula.
- You get an on-screen calculator that works like the TI-30XS, plus a whiteboard. You can't bring your own calculator.
- On the ASP, Mathematical Calculations is its own domain, worth 10% of the exam (ASP11 blueprint).
BCSP on formulas
BCSP, What to Expect When Sitting for a BCSP Exam (item 7)(opens bcsp.org in a new tab)“For any question requiring a mathematical formula, the formula will be included within the exam question (unless the question is specifically testing your knowledge of a formula). You will not be provided or permitted to bring a formula sheet.”
BCSP on calculators
BCSP, What to Expect When Sitting for a BCSP Exam (item 6)(opens bcsp.org in a new tab)“You will be provided an on-screen calculator, emulating the TI-30XS scientific calculator. You will also have access to a white board and dry erase marker. The testing center will not provide a physical calculator or permit candidates to bring their own.”
FAQ
What is the 4:1 ladder rule?
For a ladder leaning against a wall, set the foot out about 1 ft for every 4 ft of working length. In construction this comes from 1926.1053(b)(5)(i). It puts the ladder at about 75.5° from the ground.
How far should the base of a 20 ft ladder be from the wall?
If the working length from the foot to the top support is 20 ft, the base goes about 20 ÷ 4 = 5 ft out from the top support.
How far must a ladder extend above a landing?
When a portable ladder is used to reach an upper landing, the side rails must extend at least 3 ft above it. If the ladder is too short for that, secure the top to a rigid support and provide a grab rail (1926.1053(b)(1)).
Why divide the height by 0.968?
With the foot set out 1/4 of the working length, the ladder rises √(1 − 0.25²) ≈ 0.968 ft for every foot of length. Dividing the height by 0.968 gives the working length.
This tool is for study and estimates. Extension ladders are sold by overall length, and sections overlap, so check the maker's label for usable length. General industry rules are in 1910.23.