To calculate a staircase, start with the total vertical height from the finished lower floor to the finished upper floor. Divide that height into a practical number of risers, then calculate the riser height and tread depth. From there, you can estimate the total horizontal run and stair angle.
Quick method:
Measure total rise, choose a suitable number of risers, calculate riser height, choose a practical tread depth, then calculate the total run and stair angle.
For a faster calculation, use the BuildersMeasures Stair Calculator.
The exact dimensions used for a real staircase should also be checked against the building regulations and safety requirements that apply to the project location.
Table of Contents
- Stair Terms You Need to Know
- Measure the Total Stair Rise
- Calculate the Number of Risers
- Calculate Riser Height
- Calculate Tread Depth
- Calculate Total Stair Run
- Calculate Stair Angle
- Complete Stair Calculation Example
- Top and Bottom Landing
- Why Stair Headroom Matters
- Common Stair Calculation Mistakes
- Stair Calculations and Building Codes
- Stair Calculation Summary
- Frequently Asked Questions
Stair Terms You Need to Know
Several measurements are used when designing or estimating a staircase. Understanding the terms makes the calculations much easier.
| Term | Meaning |
|---|---|
| Total rise | The vertical distance from the finished lower floor to the finished upper floor. |
| Riser | The vertical portion or vertical height of one stair step. |
| Tread | The horizontal surface where the foot is placed. |
| Run | The total horizontal distance occupied by the staircase. |
| Stair angle | The angle of the stair flight measured from the horizontal. |
| Landing | A level platform at the top, bottom or between flights of stairs. |
| Headroom | The vertical clearance above the stair path. |
Measure the Total Stair Rise
The total rise is the most important starting measurement. Measure from the finished floor level at the bottom to the finished floor level at the top.
Do not measure only from the structural slab if additional flooring, tile, timber or other finishes will change the final floor levels.
Suppose the finished floor-to-floor height is 2.8 metres.
That means the staircase must climb a total vertical distance of 2.8 metres.
If the measurement is taken in millimetres, keep the units consistent throughout the calculation. For example, 2.8 metres is 2,800 millimetres.
Calculate the Number of Risers
Once the total rise is known, the next step is choosing a practical number of risers. You can estimate this by dividing the total rise by a proposed riser height.
The result is then adjusted to a whole number because a staircase cannot contain a fraction of a riser.
For a 2,800 mm total rise, suppose an initial target riser height of about 175 mm is being considered:
Sixteen risers would therefore be a possible starting point for the calculation.
The proposed riser height is not a universal value. It must be checked against the requirements that apply to the particular building.
Calculate Riser Height
After selecting the number of risers, calculate the actual riser height by dividing the total rise by that number.
Using the 2,800 mm example and 16 risers:
The calculated riser height is therefore 175 mm.
Keep risers consistent. Even a small difference between individual risers can create a noticeable change in the user's step pattern. Finished floor thicknesses should be considered before the final dimensions are established.
Calculate Tread Depth
The tread is the horizontal part of each step. A deeper tread generally provides more foot space, while a smaller tread can make a staircase steeper and less comfortable.
One common way to check a proposed stair proportion is the relationship between riser height and tread depth. A frequently used planning rule is:
This is a planning relationship, not a replacement for the requirements in the building code or standard applicable to the project.
If the riser is 175 mm and a tread of 275 mm is being considered:
The result is 625 mm, which falls within the commonly used planning range above.
The tread depth used in an actual project must still meet the applicable requirements and should account for the construction method and stair nosing details.
Calculate Total Stair Run
The total run tells you how much horizontal space the staircase will occupy.
For a straight staircase, the run can be estimated by multiplying the number of treads by the tread depth. However, the relationship between risers and treads depends on how the top and bottom floors are arranged.
In many straight flights where the upper floor forms the final step, the number of treads can be one less than the number of risers.
Suppose the staircase has 16 risers and 15 treads, with each tread 275 mm deep:
The horizontal run would be approximately 4.125 metres.
Why the one-step difference? The upper finished floor can effectively act as the final walking level. This is why a 16-riser flight may have 15 separate treads. Stair layouts with landings or different floor arrangements should be calculated according to their actual configuration.
Calculate Stair Angle
The stair angle describes how steep the flight is. It can be calculated from the total rise and total horizontal run.
The calculation uses the same basic relationship found in slope calculations.
Using the example above:
Total rise = 2,800 mm
Total run = 4,125 mm
The inverse tangent of 0.6788 is approximately 34.2 degrees.
The exact angle should be calculated from the final stair dimensions rather than assumed from a general stair type.
Complete Stair Calculation Example
Here is the complete calculation using one set of illustrative dimensions.
Given:
- Total floor-to-floor rise: 2,800 mm
- Selected number of risers: 16
- Proposed tread depth: 275 mm
Step 1: Calculate riser height
Step 2: Check the stair proportion
Step 3: Estimate the number of treads
For a simple straight flight reaching the upper floor, use 15 treads.
Step 4: Calculate horizontal run
Step 5: Estimate stair angle
This gives an illustrative staircase with 16 risers, 175 mm riser height, 15 treads at 275 mm each, approximately 4.125 metres of horizontal run and an angle of about 34.2 degrees.
These dimensions are an example of the calculation process, not a recommendation for a particular building.
Top and Bottom Landing
Landing space should be considered separately from the stair flight itself. A staircase may require a landing at the bottom, top or between flights depending on its configuration and the applicable building requirements.
A landing can affect the overall space needed for the staircase even when the calculated stair run remains unchanged.
For a U-shaped or L-shaped staircase, calculate each flight separately and include the landing dimensions when determining the total floor area required.
Why Stair Headroom Matters
Horizontal run and riser dimensions are only part of a stair layout. Headroom must also be checked to make sure people have adequate clearance as they move up the flight.
This becomes especially important when stairs pass below another floor, roof structure or landing.
A staircase can have mathematically consistent risers and treads but still fail to fit the available space because of inadequate headroom. Check the complete vertical section, not only the plan view.
Common Stair Calculation Mistakes
Measuring the wrong floor height
Using the structural floor height instead of the finished floor-to-floor measurement can change the final riser height.
Rounding the riser too early
Choose the number of risers first, then calculate the exact riser height from the total rise. Do not round each step independently.
Forgetting the difference between risers and treads
A straight staircase reaching an upper floor may have one fewer tread than risers because the upper floor forms the final walking level.
Ignoring available run
A staircase may have a suitable riser height but still require more horizontal space than the building provides.
Checking only the stair angle
The angle does not tell you everything about stair comfort or compliance. Riser height, tread depth, width, headroom, landings and other requirements also matter.
Using a generic rule as a building-code requirement
Planning formulas can help with preliminary calculations, but actual construction requirements depend on the jurisdiction, building type and applicable regulations.
Stair Calculations and Building Codes
Stair dimensions are safety-critical. The allowable riser height, minimum tread depth, stair width, handrail requirements, landing dimensions, headroom and other details can vary according to the building code or standard that applies to the project.
For that reason, a calculator should be treated as a planning and estimation tool, not as confirmation that a proposed staircase complies with local regulations.
Before construction, compare the calculated dimensions with the requirements for the project's location and building type. Where required, have the final stair design checked by an appropriately qualified building professional.
Stair Calculation Summary
| Calculation | Formula or method |
|---|---|
| Total rise | Upper finished floor level minus lower finished floor level |
| Number of risers | Total rise divided by proposed riser height, then adjusted to a whole number |
| Riser height | Total rise divided by number of risers |
| Tread depth | Selected based on layout, comfort and applicable requirements |
| Total run | Number of treads multiplied by tread depth |
| Stair angle | Inverse tangent of total rise divided by total run |
Frequently Asked Questions
How do I calculate the number of stairs I need?
Measure the total floor-to-floor rise and divide it by a proposed riser height. Adjust the result to a whole number of risers, then divide the total rise by that number to obtain the actual riser height.
How do I calculate stair riser height?
Divide the total vertical rise between finished floors by the number of risers. The resulting value is the height of each riser when the risers are evenly distributed.
How do I calculate stair tread depth?
Tread depth depends on the stair layout and applicable requirements. A common preliminary planning relationship is 2 times the riser height plus the tread depth, giving a total of approximately 600 to 650 mm.
How do I calculate the total stair run?
For a simple straight staircase, multiply the number of treads by the tread depth. The exact relationship between risers and treads depends on the stair configuration and how the upper floor is arranged.
How do I calculate stair angle?
Divide the total vertical rise by the total horizontal run and calculate the inverse tangent of that result. The resulting value is the approximate stair angle from the horizontal.
Are these stair dimensions suitable for construction?
The calculations can help with preliminary planning, but final stair dimensions should be checked against the building regulations and safety requirements that apply to the project. A qualified professional should review the final design where required.
Important: Stair calculations are useful for planning dimensions, but stairs are safety-critical construction elements. Verify the finished floor levels, proposed dimensions, headroom, landings and applicable building requirements before construction.