Stair Calculator

About the stair calculator

This free stair calculator plans a straight staircase from one number: the total rise. That is the height from the top of the lower floor to the top of the upper floor. You get the number of risers (steps up), the riser height, the tread depth, the total run, the stringer length and the angle.

A drawing of the stairs shows the same numbers. The tool also checks the headroom under the floor above, and the riser and tread against the common US code limits. If your floor space is fixed, type the total run too: the tread depth then comes from it.

Features

• Risers and treads — the number of steps and their exact size, to 1/16 inch or in cm
• Stringer — its length along the slope, the board to buy, and how many stringers your stair width needs
• A drawing — a side view of the stairs and the stringer, with the rise, run, angle and headroom on it
• Headroom check — the floor opening you need, or the headroom you get from your opening
• Code check — riser and tread against the US limits (7¾ in and 10 in), which you can change for your own code
• Comfort rule — 2 risers + 1 tread, so you see if the steps will feel natural
• Feet or metres — inches and feet, or cm and m
• Saved on this device — your numbers are still here at the lumber yard

How the stair numbers are worked out

1. Risers = total rise ÷ the highest riser you allow, rounded up. Riser height = total rise ÷ risers, so all steps are the same height.
2. Treads = risers − 1. The upper floor is the last step, so there is one tread fewer than risers.
3. Tread depth comes from the step rule (2 × riser + tread = 25 in, or 63 cm), from a size you pick, or from your total run ÷ treads.
4. Total run = treads × tread depth.
5. Angle = the angle with a slope of riser ÷ tread.
6. Stringer length = √(total rise² + total run²). The board to buy is rounded up to the next 2 ft (0.3 m).
7. Stringers = one at least every 18 in (45 cm). A 36 in wide stair needs 3.

Worked example

The page opens on a total rise of 108 in (9 ft), with risers of at most 7½ in and the step rule:

• Risers: 108 ÷ 7.5 = 14.4 → 15 risers
• Riser height: 108 ÷ 15 = 7.2 in (7 3/16 in)
• Treads: 15 − 1 = 14 treads
• Tread depth: 25 − 2 × 7.2 = 10.6 in (10 5/8 in)
• Total run: 14 × 10.6 = 148.4 in (12 ft 4 3/8 in)
• Angle: about 34.2°
• Stringer: √(108² + 148.4²) = 183.5 in (15 ft 3 9/16 in) → a 16 ft 2 × 12
• Headroom: with a 10 in thick floor above, the opening must be at least 11 ft 1/2 in long for 6 ft 8 in of headroom

With the 7¾ in limit and 10 in treads, the same height needs only 14 risers of 7 11/16 in and a total run of 10 ft 10 in. That saves floor space, but the stairs are steeper: 37.6°.

Steps for common floor heights

Risers of at most 7¾ in and treads of 10 in — the US code limits, so the shortest stairs allowed:

In metric, with risers of at most 18 cm and the step rule (2R + T = 63 cm):

Building code limits

Stairs in a home must follow the building code where you live. These are the common numbers for homes. They are only a summary: always check your own local code before you build.

The tool checks the US numbers by default. To check another code, type its numbers under Nosing, floor and code limits. In the US, treads under 11 in also need a nosing of ¾–1¼ in, and stairs must be at least 36 in wide.

Comfortable steps: the step rule

People climb stairs most easily when 2 risers + 1 tread = 24 to 25 in (about 63 cm). This old rule matches the length of a normal step. Here are treads that fit it:

Most home stairs are between 30° and 37°. Lower risers with deeper treads are easier to climb but need more floor space.

Headroom and the floor opening

Headroom is measured straight up from the line of the nosings (the front edges of the treads) to the floor or beam above. In the US it must be at least 6 ft 8 in.

Leave Floor opening above empty and the tool tells you how long the opening in the upper floor must be. Type your opening and it tells you the headroom you get. For the example stairs with a 10 in thick floor, the opening must be at least 11 ft 1/2 in. With a 10 ft opening the headroom is only 5 ft 11 1/2 in — too low.

Cutting the stringer

• Set a framing square with the riser height on the tongue and the tread depth on the blade, and mark each step along a 2 × 12.
• Cut the first riser shorter by the thickness of one tread. Then the bottom step is not taller than the others once the treads are on. The tool shows this number.
• Put stringers 18 in apart or less (45 cm). Thin or composite treads may need them closer: check what the tread maker says.
• The nosing makes each tread board deeper than the tread depth. The tool adds it for you.

Frequently asked questions

How many steps do I need for a total rise of 9 feet?

A 9 ft (108 in) total rise needs 14 risers of 7 11/16 in with the 7¾ in US limit, or 15 risers of 7 3/16 in for easier stairs. Measure from the top of the lower floor to the top of the upper floor — not the ceiling height, because the floor above adds about 10–12 in.

How do I calculate the rise and run of stairs?

Divide the total rise by the highest riser you allow and round up: that is the number of risers. Divide the total rise by that number to get the riser height. The total run is the number of treads (one fewer than risers) times the tread depth.

What is the maximum riser height?

In US homes (IRC) it is 7¾ in, with treads of at least 10 in. The UK allows 220 mm for private stairs. Other places differ, so check your local code.

How long is a stair stringer?

Use √(total rise² + total run²). For 108 in of rise and 148.4 in of run it is 183.5 in (15 ft 3 9/16 in), so you buy a 16 ft board.

What angle should stairs be?

Most home stairs are between 30° and 37°. The example on this page is 34.2°. Above about 42° stairs feel like a ladder, and the UK does not allow them for homes.

How much headroom do stairs need?

At least 6 ft 8 in in the US and 2.0 m in the UK and Germany, measured straight up from the nosing line. The tool works out the floor opening you need for it.

Can I use metres and centimetres?

Yes. Switch to Metres & cm. The step rule then uses 63 cm, and risers and treads are shown in cm.

Related tools

• Deck Calculator — boards, joists and posts for the deck at the top of the stairs
• Concrete Calculator — concrete steps or a landing pad
• Board Foot Calculator — the lumber for stringers and treads
• Roofing Calculator — slope and pitch work the same rise-over-run way
• Unit Converter — inches, feet and centimetres

How to use it

• Choose Feet & inches or Metres & cm
• Type the total rise: from the top of the lower floor to the top of the upper floor, like 108 or 9'
• If your floor space is fixed, type the total run too
• Pick the highest riser height and a tread depth (or keep the step rule)
• Type the stair width to count the stringers, and the floor opening to check the headroom
• Read the risers, treads, stringer and angle, look at the drawing, and press Copy the list