Stair Calculator: Number of Risers, Riser Height, Going, 2R+G Rule and Stringer Length

Divide a floor-to-floor height into equal steps and check that the stair is comfortable and within the usual limits.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the total rise from one floor to the next, the biggest riser you will allow and the going of the treads.

The calculator finds the fewest risers that keep each riser within the limit, the height of each riser, the number of treads (one fewer than the risers), the total run, the pitch and the length of the stringer.

It checks 2R + G is between 550 and 700 mm and the riser and going against the NCC limits for a house stair. For a ramp, enter the gradient to get the length.

Formulas used

  • n = \lceil H / R_{max}\rceil,\quad R = H / n
  • n_t = n - 1
  • 2R + G = 550\text{ to }700\ \mathrm{mm}
  • L_s = \sqrt{H^2 + \text{run}^2}

Worked example

With the default numbers in the calculator above:

  1. Number of risers (the fewest that keep each riser within the limit): 15 risers
  2. Height of each riser: 180.00 mm
  3. Number of treads (one fewer than the risers, because the upper floor is the last tread): 14 treads
  4. Total run of the stair: 3500.00 mm (3.50 m)
  5. The comfort rule 2R + G (usually between 550 and 700 mm): 610.00 mm
  6. Pitch of the stair: 35.75 degrees
  7. Length of the stringer along the slope: 4420.41 mm (4.42 m)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? A ramp.

  1. Length of the ramp along the ground: 37.80 m (37800.00 mm)
  2. Length of the surface of the ramp: 37.90 m
  3. Gradient as a percentage and an angle: 7.14 percent, 4.09 degrees

Common questions

Why is there one tread fewer than risers?

The top of the last riser meets the upper floor, which acts as the last tread.

What is the 2R + G rule?

Two risers plus a going should come to between about 550 and 700 mm, which suits the length of a human pace.

What are the NCC limits for a house stair?

Riser 115 to 190 mm and going 240 to 355 mm, with a 2R + G of 550 to 700 mm. Other building classes differ, so check the code.

What gradient can a ramp have?

An accessible ramp is no steeper than 1 in 14 under AS 1428.1, with landings, handrails and edge protection.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: National Construction Code (stairways and ramps); AS 1428.1 Design for access and mobility; AS 1657 Fixed platforms, walkways, stairways and ladders.

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