Math

Ladder Length & Height Calculator

Calculate Ladder Reach and Safe Placement

Use the Pythagorean theorem to calculate how high a ladder reaches or what ladder length you need. The OSHA 4:1 rule recommends the base distance be one-quarter of the working height, producing a 75.5-degree contact angle. Enter the ladder length as the hypotenuse and the base distance as one leg.

Pythagorean Theorem Tips

Click to show tips

Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Ladder Against Wall

A 10-foot ladder leans against a wall with the base 6 feet away. How high does it reach?

Key values: Leg a = 6 ft · Hypotenuse c = 10 ft · Solve for leg b

TV Screen Diagonal

Find the diagonal of a TV with a 16:9 aspect ratio (width 40", height 22.5").

Key values: Width = 40 in · Height = 22.5 in · Find diagonal

Classic 3-4-5 Triangle

Verify that sides 3, 4, and 5 form a right triangle (the most famous Pythagorean triple).

Key values: Sides: 3, 4, 5 · Right triangle · Primitive triple

Documentation

This calculator is also known as Ladder Length & Height Calculator.

Read the complete guide

OSHA Ladder Safety

The OSHA 4:1 rule states that for every 4 feet of working height, the ladder base should be 1 foot from the wall. This creates a contact angle of approximately 75.5 degrees, which is the safest angle for ladder stability.

Examples

Reaching a 20 ft Roof

A 20 ft ladder is placed 5 ft from the wall. How high does it reach?

Height = √(20² - 5²) = √(400 - 25) = √375 ≈ 19.36 ft.

Key takeaway: The ladder reaches about 19.4 ft, well within the OSHA recommended angle.

Ladder Safety Checklist

Follow these safety steps:

Use the 4:1 rule: base distance = working height / 4
The ladder should extend 3 ft above the landing point
Always have three points of contact when climbing
Never exceed the ladder rated load capacity

Frequently Asked Questions about Ladder Length & Height Calculator

What is the OSHA 4:1 ladder rule?

For every 4 feet of height the ladder reaches, the base should be 1 foot away from the wall. This creates a contact angle of approximately 75.5 degrees, which OSHA considers the safest placement angle.

How do I calculate what size ladder I need?

Enter the height you need to reach as one leg and the planned base distance as the other leg. The hypotenuse (c) is the minimum ladder length required. Add 3 feet for overlap past the landing point.

What angle should a ladder be placed at?

OSHA recommends a 75.5-degree contact angle, achieved by the 4:1 rule: for every 4 feet of height, place the base 1 foot from the wall. Steeper angles risk the ladder tipping backward; shallower angles risk the base sliding out.