Stair Calculator with Diagram

Calculate stair rise, run, angle, stringer length, and step dimensions. Visual diagram included. Meets IRC building codes.

Vertical distance between finished floors
Leave blank to calculate based on riser height
Building code: 4" min, 7.75" max
Building code: 10" min (with nosing)
Typically 0.75" to 1.25"

Stair Diagram

Diagram shows stair profile with dimensions

Stair Dimensions

Number of Steps: -
Riser Height: -
Tread Depth: -
Total Run: -
Stringer Length: -
Stair Angle: -

Building Code Check

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Material Estimates

Stringer Board Length: -
Tread Material (sq ft): -
Riser Material (sq ft): -

Step-by-Step Calculation

Enter total rise and desired riser height, then click "Calculate Stairs" to see the step-by-step solution.

Stair Formulas

  • Step Count: N = Rise / Riser Height
  • Total Run: Run = Tread × (N - 1)
  • Stringer Length: √(Rise² + Run²)
  • Stair Angle: arctan(Rise / Run)
  • Riser Height: Rise / N

IRC Building Code Requirements

  • Riser Height: 4" min, 7.75" max
  • Tread Depth: 10" min (with nosing)
  • Stair Width: 36" min (residential)
  • Headroom: 80" minimum
  • Rise + Run: 17" to 18" total

Comfortable Stair Formula

  • 2R + T = 24" to 25" (Blondel's Formula)
  • R = Riser Height, T = Tread Depth
  • If total is 24-25", stairs are comfortable
  • Example: 2×7.5 + 10 = 25" ✓

Frequently Asked Questions

How do I calculate stairs?

To calculate stairs: (1) Divide total rise by desired riser height to get number of steps. (2) Multiply tread depth by (number of steps - 1) to get total run. (3) Use Pythagorean theorem to find stringer length.

What is the standard stair rise and run?

Standard residential stairs have a riser height of 7-7.5 inches and tread depth of 10-11 inches. The formula 2R + T should equal 24-25 inches for comfortable stairs.

What is code for stair risers?

According to IRC (International Residential Code), riser height must be between 4 inches (minimum) and 7.75 inches (maximum). All risers should be within 3/8" of each other.

How do you calculate stair stringer length?

Stringer length = √(total rise² + total run²). For a deck with 40" rise and 60" run: √(40² + 60²) = √(1600 + 3600) = √5200 = 72.1 inches.

What is the formula for number of stairs?

Number of steps = total rise ÷ desired riser height. Round to nearest whole number. Then actual riser height = total rise ÷ number of steps.

How much headroom do stairs need?

IRC requires a minimum of 80 inches (6'8") of headroom above the stair treads to the ceiling. Measure vertically from the nosing line.