CodingAce
Ladders
Advanced
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Angles from ground; angle from wall = 90° − θ. Ensure inputs are feasible.
Results
Ladder length (L)
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Base distance (b)
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Vertical reach (h)
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Lean angle θ (ground)
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Angle from wall
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Slope m = h / b
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Grade (%)
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Base : Height
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Height : Base
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4:1 rule deviation
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| Units | L | b | h | θ (deg) | m = h/b | Grade (%) | b:h | 4:1 deviation |
|---|
Angle diagram
Shows base distance, reach, and lean angle θ at ground. Includes 4:1 base marker.
Formula used
Let ladder length L, base distance b, vertical reach h, lean angle from ground θ (radians), angle from wall α = \u03C0/2 - θ.
b = L \u22C5 \u2061 \u2192 \u2061 \cos(θ),h = L \u22C5 \u2061 \sin(θ)L = \u221A(b^2 + h^2),θ = \u2061 \mathrm{atan2}(h, b)m = h/b, grade percent= 100 \u00D7 m- 4:1 guideline: recommended base
b_{rule} = h/4, target angle ≈75.5°
All outputs reflect your selected units. Rounded for display; internal calculations keep precision.
How to use
- Select units.
- Choose which values you already know.
- Enter the numbers and press Calculate.
- Review computed distances, angles, slope, and rule checks.
- Download your results as CSV or PDF.
This tool aids planning only. Use proper training and site-specific safety practices.
Example data table
| Scenario | Units | L | b | h | θ | b:h | 4:1 deviation |
|---|---|---|---|---|---|---|---|
| Typical exterior | ft | 24 | 6.0 | 23.2 | 75.5° | 1:3.9 | near target |
| Compact indoor | m | 3.5 | 0.85 | 3.39 | 78.6° | 1:4.0 | slightly steep |
| Shallow lean | m | 4.0 | 1.6 | 3.68 | 66.5° | 1:2.3 | too shallow |
FAQs
It’s a common guidance: for every four units of vertical height, set the ladder base one unit out from the wall, yielding a lean angle near 75.5°.
It shows the lean angle from the ground (θ) and the complementary angle from the wall (α = 90° − θ), together with slope and grade percent.
Yes. Choose one of four modes: L+θ, L+b, L+h, or b+h. The calculator computes the remaining quantities and validates geometric feasibility automatically.
Slope m is the ratio h/b. Grade percent is 100 × m. They express the same steepness in different units for convenience and industry familiarity.
No. It’s a planning aid only. Always consult manufacturer instructions, site policies, and applicable regulations. Ensure firm footing, proper extension above landings, and trained supervision.
Yes. Use the Download CSV and Download PDF buttons inside the Results card. CSV contains tabular outputs; PDF captures a formatted summary.