Excavation slope calculator
- Formula: horizontal run = depth × H:V ratio
- Type C soil: maximum allowable slope is 1½:1 (34°), so the ratio is 1.5 ft across for every 1 ft down.
- Put in the numbers: 12 ft × 1.5 = 18 ft on each side
- Top width = bottom width + 2 × run: 4 + 2 × 18 = 40 ft
- Answer: slope back at least 18 ft horizontally on each side
Formula and sources
- Horizontal run = depth × H:V ratio
- Stable rock vertical, Type A 3/4:1, Type B 1:1, Type C 1½:1
- Top width = bottom width + 2 × run
The formula comes from
29 CFR 1926 Subpart P, Appendix B (Figure B-1)(opens ecfr.gov in a new tab)“All simple slope excavation 20 feet or less in depth shall have a maximum allowable slope of 3/4:1. ... All simple slope excavations 20 feet or less in depth shall have a maximum allowable slope of 1:1. ... All simple slope excavations 20 feet or less in depth shall have a maximum allowable slope of 1 1/2:1.”
The formula comes from
29 CFR 1926 Subpart P, Appendix B, (c)(2), (c)(3)(ii) and B-1.1 exception(opens ecfr.gov in a new tab)“The maximum allowable slope for a soil or rock deposit shall be determined from Table B-1 of this appendix. ... the slope shall be cut back to an actual slope which is at least 1/2 horizontal to one vertical (1/2H:1V) less steep than the maximum allowable slope. ... Simple slope excavations which are open 24 hours or less (short term) and which are 12 feet or less in depth shall have a maximum allowable slope of 1/2:1.”
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
How far back do I slope a trench?
Multiply the depth by the horizontal part of the maximum allowable slope. Type A is 3/4:1, Type B is 1:1 and Type C is 1½:1. A 12 ft deep trench in Type C soil needs 12 × 1.5 = 18 ft of horizontal run on each side.
What does 1½:1 mean?
It's horizontal to vertical (H:V). For every 1 ft of depth, the face goes back 1.5 ft. Appendix B defines the maximum allowable slope as the ratio of horizontal distance to vertical rise.
Can Type A soil be steeper?
Yes, for a short-term simple slope. Appendix B allows 1/2:1 (63°) in Type A when the excavation is open 24 hours or less and is 12 ft or less deep.
What if the trench is deeper than 20 ft?
Appendix B only covers excavations 20 ft or less deep. Deeper sloping or benching has to be designed by a registered professional engineer.
What if the soil shows signs of distress?
The slope must be cut back to at least 1/2H:1V less steep than the maximum allowable slope, per Appendix B (c)(3)(ii).
This tool is for study and estimates. A competent person must classify the soil and inspect the excavation. It doesn't cover benching, layered soils or surcharge loads.