A leaning ladder makes a right triangle with the wall and the ground, so its length is L = √h2 + b2, where h is the height of the top support and b is the distance from the wall to the feet. To rest a ladder 16 ft up with its feet 4 ft out, you need √256 + 16 ≈ 16.49 ft of ladder.
How to use the ladder calculator
- Enter the two values you know. Height and base give the ladder length you need; length and base give the reach; length and height tell you where to put the feet.
- Measure the height to the support point, where the ladder actually rests (a roof edge, the top of a wall, a landing), not to the top of the ladder.
- Read the angle check. Green means the setup is close to the 4-to-1 rule; amber means too steep or too shallow, with the fix. The last tile adds the 3 ft (0.9 m) needed to step onto a roof.
The ladder formulas
The wall and the ground meet at a right angle, so together with the ladder they form a right triangle. The wall is one leg of the triangle, the ground is the other and the ladder is the hypotenuse, the side opposite the right angle at the foot of the wall. The Pythagorean theorem gives each side from the other two:
L= √h2 + b2h= √L2 − b2b= √L2 − h2The angle θ between the ladder and the ground comes from trigonometry (see when to use the theorem and when to use trig): θ = arctan(h ÷ b), or equivalently cosθ = b ÷ L. The ladder is always the longest side, so the calculator refuses a height or base distance that is longer than the ladder. To work from the ladder length and an angle instead, use the right triangle calculator; for any other pair of sides, the general Pythagorean theorem calculator.
The 4-to-1 rule explained
For straight and extension ladders that lean on a support, the standard rule is one out for every four along. The US Occupational Safety and Health Administration (OSHA) puts it this way for construction work: set the ladder so the horizontal distance from the top support to the foot is about one quarter of the ladder's working length. That fixes the angle, whatever the size of the ladder:
cosθ= b over L = 1 over 4θ= arccos(1 over 4) ≈ 75.5°You will also hear the rule as "1 ft out for every 4 ft of height". That version measures the 4 up the wall rather than along the ladder, giving arctan4 ≈ 76.0°. The two differ by less than half a degree, and both land on the roughly 75° angle that ladder makers and the American National Standards Institute (ANSI) ladder standards recommend. The calculator follows the OSHA wording and marks a setup green when the base is within about 10% of one quarter of the ladder length, which is an angle between roughly 74° and 77°.
The angle is a compromise. A ladder set too steep can tip backward when you lean or reach, because your weight ends up close to the line through the feet. Set it too shallow and the feet can slide out, and the ladder bends more under load. About 75° balances the two.
| Working length | Base distance (¼ of length) | Height reached |
|---|---|---|
| 8 ft | 2 ft | 7.75 ft |
| 12 ft | 3 ft | 11.62 ft |
| 16 ft | 4 ft | 15.49 ft |
| 20 ft | 5 ft | 19.36 ft |
| 24 ft | 6 ft | 23.24 ft |
| 28 ft | 7 ft | 27.11 ft |
| 32 ft | 8 ft | 30.98 ft |
| 4 m | 1 m | 3.87 m |
| 6 m | 1.5 m | 5.81 m |
At this angle a ladder reaches √15 ÷ 4 ≈ 0.968 of its working length up the wall, so a quick estimate is "height ≈ 97% of the ladder". Extension ladders are sold by their total length, but their sections overlap, so the working length you can actually use is shorter than the number on the side. Check the label before you compare it with the calculator's answer.
Reaching a roof or a landing
When you use a ladder to step onto a roof, a platform or another landing, the side rails should extend at least 3 ft (0.9 m) above the landing so you have something to hold as you step on and off. OSHA's construction rule says the same; where the ladder is too short for that, it must be secured at the top to a rigid support and a grab rail provided. In practice it means you need 3 ft more ladder than the triangle alone suggests. Builders size stairs, ramps and braces with the same triangle; see the Pythagorean theorem in construction.
Worked examples
Example 1: how long a ladder to reach 20 ft?
The top support is 20 ft up. At the 4-to-1 angle the height is √15 ÷ 4 of the working length, so
L= 4 × 20 over √15 ≈ 20.66 ftb= L over 4 ≈ 5.16 ftAbout 20.7 ft of working length with the feet about 5.2 ft out. With the rule-of-thumb version (5 ft out for 20 ft up) you get √202 + 52 = √425 ≈ 20.62 ft, nearly the same. Add 3 ft if you are stepping onto a roof at that height.
Example 2: how high does a 24 ft ladder reach?
A 24 ft working length with the feet 6 ft from the wall:
h= √242 − 62 = √576 − 36= √540 = 6√15 ≈ 23.24 ftIt reaches about 23.24 ft, and since 6 ÷ 24 = 1 over 4 exactly, the angle is the ideal 75.5°.
Example 3: a setup that fails the check
A ladder reaches 15 ft up the wall with its feet 8 ft out.
L= √152 + 82 = √225 + 64= √289 = 17 ftθ= arctan(15 ÷ 8) ≈ 61.9°The base is 8 ÷ 17 ≈ 0.47 of the ladder, almost double the 0.25 the rule asks for, so the angle is far too shallow. For a 15 ft support, the 4-to-1 setup uses about 15.49 ft of ladder with the feet 3.87 ft out. (8-15-17 is a Pythagorean triple, which is why the length came out whole.)
Ladder questions are classic exam problems too; practice more on the word problems page.
Ladder setup checklist
The math gives the length and the angle. These general habits matter just as much; always follow your ladder's label and any workplace rules that apply to you.
- Feet on firm, level ground, and the top resting on a solid surface, not a window pane or a gutter that could give way.
- Set the angle with the 4-to-1 rule. A common field check: stand with your toes against the ladder's feet and hold your arms straight out; your palms should just reach a rung at about shoulder height.
- Extend 3 ft above a landing you are climbing onto, and tie off or secure the ladder where it could slip.
- Look up first. Keep ladders well away from overhead power lines, especially metal ones, which conduct electricity.
- Face the ladder and keep three points of contact (two hands and a foot, or two feet and a hand) while climbing, and do not overreach to the side.
- Check the duty rating. Your weight plus tools and materials must stay within the load printed on the label.
NoteThe 4-to-1 rule is for ladders that lean against a support. A stepladder supports itself and should be used fully opened with its spreaders locked, never folded and leaned against a wall.
Frequently asked questions
What is the 4-to-1 rule for ladders?
For every 4 ft of ladder between the feet and the top support, set the feet 1 ft out from the wall. That puts the ladder at about 75.5° to the ground. People also say "1 ft out for every 4 ft up", which gives about 76°; either way the angle is close to 75°.
What angle should a ladder be at?
About 75° from the ground; the exact 4-to-1 angle is arccos(1/4) ≈ 75.5°. The calculator accepts roughly 74° to 77° as close enough and suggests a correction outside that range.
How long a ladder do I need to get onto a roof?
Measure the height of the roof edge, find the ladder length for that height at the 4-to-1 angle (about 1.033 times the height), then add 3 ft. For a 12 ft edge: 12 × 4 ÷ √15 ≈ 12.39 ft, plus 3 ft, so about 15.4 ft of working length.
Why is the ladder the hypotenuse?
The wall and the ground meet at a right angle, so they are the two legs, and the ladder spans the gap between them, opposite that right angle. The hypotenuse is always the longest side, which is why a ladder can never reach as high as its own length unless it stands straight up.
Sources and further reading
- OSHA, 29 CFR 1926.1053, Ladders (construction industry): the one-quarter rule for non-self-supporting ladders and the 3 ft extension above landings.
- American National Standards Institute, ANSI A14 series of standards for portable ladders.
Keep exploring
- PracticePythagorean Theorem Word Problems15 Pythagorean theorem word problems from real life (ladders, TVs, ramps, ships, kites, roofs) with a 4-step strategy, a sketch for each and full solutions.
- CalculatorsPythagorean Theorem CalculatorFree Pythagorean theorem calculator. Enter any two sides of a right triangle to find the third, with step-by-step working, exact radical answers and a drawing.
- Real-life usesThe Pythagorean Theorem in ConstructionHow builders use the Pythagorean theorem: the 3-4-5 rule for squaring corners and foundations, diagonal checks, stairs, rafters, ramps, braces and field tips.
- CalculatorsRafter Length and Roof Pitch CalculatorRafter length and roof pitch calculator. Enter the run and the pitch, rise or angle to get rafter length with overhang, roof angle, slope percent and slope factor.
- CalculatorsRight Triangle Calculator and SolverRight triangle solver: enter any two values, such as two sides or a side and an angle, to get all three sides, both angles, area, perimeter, altitude and radii.
- LearnPythagorean Theorem or Trigonometry: Which Should You Use?When to use the Pythagorean theorem vs trigonometry (SOH CAH TOA): a decision flowchart, side-by-side worked examples and multi-step problems that need both.