Enter the number of steps, tread depth, and height of each step into the calculator to determine the staircase length.

Staircase Length Formula

The following formula is used to calculate the length of a staircase.

SL = sqrt((N^2 * T^2) + (N * H^2))


  • SL is the staircase length (inches) N is the number of steps T is the tread depth (inches) H is the height of each step (inches)

To calculate the staircase length, square the number of steps and multiply by the square of the tread depth. Then, multiply the number of steps by the square of the height of each step. Add these two results together and take the square root of the sum. This will give you the length of the staircase.

What is a Staircase Length?

Staircase length refers to the total distance or number of steps taken to traverse a staircase from the bottom to the top. It is often used in mathematics or computer science to describe the number of steps in a process or algorithm. The staircase length can vary depending on the size of the steps or the height of the staircase. It can also be used metaphorically to describe the complexity or length of a task or process.

How to Calculate Staircase Length?

The following steps outline how to calculate the Staircase Length using the given formula:

  1. First, determine the number of steps (N).
  2. Next, determine the tread depth (T) in inches.
  3. Next, determine the height of each step (H) in inches.
  4. Next, substitute the values of N, T, and H into the formula: SL = sqrt((N^2 * T^2) + (N * H^2)).
  5. Finally, calculate the Staircase Length (SL).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

Number of steps (N) = 10

Tread depth (T) = 12 inches

Height of each step (H) = 6 inches