THE NUMBERS, EXPLAINED
How to use this calculator.
Gradient is rise divided by horizontal run. This does not assess accessibility or building standards.
Start with your inputs
Enter rise (m), horizontal run (m). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Rise (m) | 1 |
| Horizontal run (m) | 12 |
A worked example
With the example inputs above, gradient (%) is 8.333333. Change the inputs to explore your own scenario.
Putting the example numbers into the formula
Gradient (%)
(1) ÷ (12) × 100 = 8.333333
Angle (degrees)
atan((1) ÷ (12)) × 180 ÷ π = 4.763642
| Result | Example answer |
|---|---|
| Gradient (%) | 8.333333 |
| Angle (degrees) | 4.763642 |
How this is calculated
Gradient (%)
a ÷ b × 100
Angle (degrees)
atan(a ÷ b) × 180 ÷ π
Symbols and units
- a
- Rise (m)
- b
- Horizontal run (m)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Calculation steps and notation
atan returns the inverse tangent in radians. Multiply by 180/π for degrees.
π is the circle constant, approximately 3.141592653589793.
Assumptions and limits
Gradient is rise divided by horizontal run. This does not assess accessibility or building standards.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Gradient (%); Angle (degrees). The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Gradient is rise divided by horizontal run. This does not assess accessibility or building standards.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
Read the quality report →