Stair Stringer Calculator

Building deck stairs?

For outdoor stairs attached to a deck, use the dedicated deck stair calculator — same stringer math, plus deck-specific guidance on measuring at the landing, concrete pads, stringer hangers, and the handrail and guard thresholds that apply to decks.

If you already know your step count, the stringer dimension tables by step count give pre-computed rise, run, length, and angle for 2 to 16 steps. If you are still planning the build sequence, read the deck stair stringer layout guide; for code context, check the stair rise and run code requirements.

Check stair rise and run limits

The International Residential Code (IRC) sets the limits for residential stair dimensions. The maximum rise per step is 7¾ inches (IRC R311.7.5.1), and the minimum tread depth is 10 inches (IRC R311.7.5.2). These limits keep stairs safer and easier to walk on. Commercial stairs fall under the stricter IBC: 7" maximum rise and 11" minimum tread.

A practical guideline is the comfort rule: the sum of one rise plus one tread should fall between 17 and 18 inches. A 7.5" rise with a 10.5" tread gives you 18" — right at the top of the comfort zone.

This calculator selects a step count that keeps rise per step within the IRC maximum when possible. If tread depth is below 10", or if rise plus run falls outside the comfort range, the result panel shows a warning. Always verify your local code, permit requirements, landing details, and handrail requirements before building.

Stair stringer formula: rise, run, total run, and length

The stair stringer math starts with total rise and your desired tread depth. From those two inputs, you can calculate step count, actual rise, total run, stringer length, and cut angle.

Here is the step-by-step process, using a 108-inch (9-foot) floor-to-floor rise with a 10.5-inch tread depth:

1. Determine step count. Divide total rise by the target rise of 7.5 inches: 108 / 7.5 = 14.4, which rounds to 14 steps. Verify that the actual rise (108 / 14 = 7.71") does not exceed the 7.75" IRC maximum.
2. Calculate rise per step. Divide total rise by step count: 108 / 14 = 7.714 inches per step. This is the measurement you'll mark on your framing square.
3. Calculate total run. Multiply tread depth by (steps − 1): 10.5 × 13 = 136.5 inches. There's one fewer tread than risers because the top step lands on the upper floor.
4. Calculate stringer length. Use the Pythagorean theorem: √(108² + 136.5²) = √(11664 + 18632.25) = √30296.25 ≈ 174.1 inches (about 14.5 feet).
5. Determine cut angle. The angle from horizontal is arctan(rise/run) = arctan(7.714/10.5) ≈ 36.3°. This is the angle your stringer makes with the floor.

The calculator above handles all this math automatically. Enter your total rise and tread depth, and it returns every measurement you need to lay out and cut your stringers.

Cutting your stringers

Once you have your rise and run measurements, follow these steps to lay out and cut the stringer:

1. Set up your framing square. Clamp stair gauges to the square at the rise measurement on the tongue (short side) and the run measurement on the blade (long side). These gauges ensure every notch is identical.
2. Mark the first step. Place the square on the stringer board with both gauges against the top edge. Draw a line along both the tongue and blade — this marks one rise and one run.
3. Walk the square down the board. Slide the square until the blade gauge aligns with the end of the previous rise line. Mark again. Repeat for all steps.
4. Adjust for the bottom riser. The bottom riser needs to be shortened by one tread thickness (typically ¾" for standard decking or 1" for hardwood treads). This accounts for the tread that sits on top of the first step. Measure and mark the reduction from the bottom cut line.
5. Cut the notches. Use a circular saw to cut along the rise and run lines, stopping just short of the inside corner. Finish the inside corners with a handsaw or jigsaw to avoid overcutting. Overcutting weakens the stringer.
6. Check remaining material. After cutting, the narrowest part of the stringer (the "throat") must be at least 3.5 inches wide for a 2×12. This ensures structural integrity.

Always cut one stringer first and test-fit it before cutting the rest. Use it as a template for consistent results.