How do you calculate the volume of concrete for stairs?

For a solid concrete staircase, the volume is calculated as: Volume (m³) = width × tread depth × rise × n(n+1)/2, where n is the number of steps. This formula accounts for the triangular fill of material that builds up under each successive step. For example, 5 steps with a 175 mm rise, 300 mm tread and 1,200 mm width gives: 1.2 × 0.30 × 0.175 × (5 × 6 / 2) = 1.2 × 0.30 × 0.175 × 15 = 0.945 m³. Always add 10% waste to your order.

What is the standard rise and tread for concrete stairs in NZ?

New Zealand Building Code clause D1 (Access routes) and NZS 4121 set out requirements for stair dimensions. For residential exterior stairs, a common comfortable proportion follows the rule 2R + G = 600 mm to 700 mm, where R is the rise and G is the going (tread). Standard dimensions are typically a rise of 150 mm to 190 mm and a going of 250 mm to 300 mm. For most residential outdoor concrete steps, a rise of 175 mm and tread of 300 mm is a widely used combination.

How many 20 kg bags of concrete mix does a staircase need?

A standard 20 kg bag of ready-mix concrete yields approximately 0.009 m³ (9 litres) of finished concrete. Divide your total volume (in m³) by 0.009 to get the number of bags, then add 10 percent for waste. For example, 0.945 m³ needs 0.945 ÷ 0.009 = 105 bags before waste, so order approximately 116 bags. For larger volumes it is usually more economical to order ready-mix concrete delivered by truck (typically sold per cubic metre).

Concrete Stairs Calculator

Calculate the volume of concrete needed for a solid concrete staircase, the number of bags required, and an estimated material cost. Enter the number of steps, rise height, tread depth and stair width to get instant results.

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Updated June 2026 Formula: solid staircase volume = width × tread × rise × n(n+1)/2. NZ Building Code D1 step proportions.

1. Stair Dimensions

Number of steps

Rise (height of each step) mm

Tread depth (going per step) mm

Stair width mm

2. Material Options

Bag size

Waste allowance

Cost per bag NZD (optional)

Or: ready-mix cost $/m³ optional

$/m³

Concrete Required

Total Volume
-
m³ (incl. waste)

Bags Needed

incl. waste

Bag Cost (est.)

materials only

Ready-Mix Cost (est.)

materials only

Volume Breakdown

Number of steps-

Rise per step-

Tread depth-

Stair width-

Net concrete volume-

Waste allowance-

Volume to order-

Stair Geometry

Total rise (height)-

Total run (horizontal)-

Stringer length (approx)-

2R + G (comfort check)-

Bag size selected-

Bags (net, no waste)-

Bags to buy (incl. waste)-

Volume Per Step

Step	Cumulative height	Volume for this step (m³)	Running total (m³)

Summary: Enter your stair dimensions above to see results.

How to Calculate Concrete for Stairs

A solid concrete staircase is poured as a monolithic structure. Unlike timber stairs where each step is independent, a concrete staircase fills all the material beneath each step as well. This means the bottom step requires concrete for its full height, and each step above it adds another layer of material on top of what is already there.

The volume formula for a solid concrete staircase is:

Volume (m³) = width × tread × rise × n(n+1) / 2

Where n is the number of steps. This is derived from the sum of the series 1 + 2 + 3 + ... + n = n(n+1)/2. Each step contributes a rectangular prism equal to the tread depth multiplied by the accumulated height up to that step, multiplied by the stair width.

Worked Example

Using the default values: 5 steps, 175 mm rise, 300 mm tread, 1,200 mm width.

Dimension	Value	In metres
Number of steps (n)	5	-
Rise	175 mm	0.175 m
Tread	300 mm	0.300 m
Width	1,200 mm	1.200 m
n(n+1)/2	5 × 6 / 2 = 15	-
Net volume	1.2 × 0.3 × 0.175 × 15	0.945 m³
+ 10% waste	0.945 × 1.10	1.040 m³
20 kg bags (0.009 m³ each)	1.040 / 0.009	116 bags

NZ Stair Proportions

The New Zealand Building Code (Clause D1: Access routes) and NZS 4121 set minimum and maximum dimensions for stairs. A common comfort rule used in residential design is:

2R + G = 600 mm to 700 mm (where R = rise, G = going/tread)

Rise (mm)	Going (mm)	2R + G	Comfort rating
150	300	600	Good (shallow)
175	300	650	Ideal residential
190	260	640	Acceptable
200	250	650	Steeper

For outdoor residential concrete stairs, a rise of 150 mm to 175 mm and going of 280 mm to 330 mm is most common. Avoid a rise greater than 190 mm or a going less than 250 mm for frequently used external stairs.

Bags vs Ready-Mix

For small staircases (under about 0.5 m³), bagged concrete mix is convenient. For volumes above 0.5 m³, ordering ready-mix concrete delivered by truck is usually more economical per cubic metre, though minimum delivery charges apply (typically 0.3 m³ to 1.0 m³ minimums depending on the supplier). Ready-mix also allows you to specify the concrete strength (for example, 25 MPa is commonly specified for residential concrete stairs).

Formwork Tips

Build formwork from 18 mm plywood or 100 mm timber boards staked firmly in place.
Oil or wet the formwork before pouring to prevent adhesion.
Pour from the bottom step upwards and compact each layer with a rod or vibrator.
For stairs wider than 1.5 m, add a central stringer for extra formwork support.
Cure the concrete by keeping it damp for at least three days, especially in hot or windy weather.
Do not apply loads for at least 24 hours; leave formwork in place for at least 48 hours.

Related Calculators

Science and Engineering Calculators: all building and trades tools in one place.
Concrete Bags Needed Calculator: general concrete volume to bags converter.
Stair Calculator: rise, run and stringer length for any staircase type.
Cost of a Deck or Fence All-In Calculator: outdoor structure cost estimates.
Concrete Calculator: volume for slabs, footings and pads.

Sources and method: Volume formula derived from the geometric series sum for a solid staircase (each step is a rectangular prism of width × tread × cumulative rise). NZ Building Code Clause D1 Access Routes (Ministry of Business, Innovation and Employment). NZS 4121:2001 Design for access and mobility. Bag yield based on standard NZ product data sheets (approximately 0.009 m³ per 20 kg bag of premixed concrete).

This calculator gives indicative material quantities only. Actual concrete volumes depend on stair geometry, formwork accuracy, and pour method. Always confirm quantities with your concrete supplier. Prices shown are estimates only and vary by region and supplier. This tool does not account for landing slabs, reinforcement, or sub-base preparation.