How to calculate gradient from rise and run
Gradient compares vertical change with horizontal travel. A rise of 1 m over 20 m means the height changes by 0.05 m for every horizontal metre.
What the formula is saying
Divide the elevation change Δh by horizontal distance L. This gives a ratio; multiply by 100 for percent grade. It is not an angle in degrees.
Read the symbols in plain language
- Δh
- Elevation changem
- L
- Horizontal lengthm
Sort out the units first
Use the same length unit for rise and run. 1 m / 20 m = 0.05 = 5%. For a nonzero magnitude, “1 in n” uses n = 1/|S|.
Let’s solve one together
Read the given values, follow each operation, then check what the result means.
- Δh · Elevation change
- 1 m
- L · Horizontal length
- 20 m
Find the signed elevation change
Final elevation minus initial elevation sets uphill or downhill sign.
(1) = 1 mDivide by horizontal run
The length units cancel and leave a slope ratio.
(1) ÷ (20) = 0.05Express the gradient as percent
The calculator reports percent grade, not degrees or a slope ratio.
(0.05) × 100 = 5 %
Does this worked answer make sense?
Multiply ratio by run to recover rise: 0.05 × 20 = 1 m. A downhill elevation change gives a negative ratio.
Now try your own values
Change a value or its unit. The same method will show your calculation, step by step.
Results update only when you calculate. The lesson example above stays unchanged.
Your turn — check your understanding
Use these new values. Work it out first, then check your answer.
- Δh · Elevation change
- 0.6 m
- L · Horizontal length
- 30 m
Find: gradient from rise and run
A hint, not the answer
Divide the elevation change Δh by horizontal distance L. This gives a ratio; multiply by 100 for percent grade. It is not an angle in degrees.
Use the same length unit for rise and run. 1 m / 20 m = 0.05 = 5%. For a nonzero magnitude, “1 in n” uses n = 1/|S|.
Show the full practice solution
Compare the steps with your work; revealing a solution does not mark the lesson complete.
Find the signed elevation change
Final elevation minus initial elevation sets uphill or downhill sign.
(0.6) = 0.6 mDivide by horizontal run
The length units cancel and leave a slope ratio.
(0.6) ÷ (30) = 0.02Express the gradient as percent
The calculator reports percent grade, not degrees or a slope ratio.
(0.02) × 100 = 2 %
Avoid the common trap
A gradient of 0.05 is 5%, not 0.05%. Use horizontal run, not slope length, for this definition.
When this method applies — and when it does not
Geometric slope calculation only. This does not establish a permitted ramp, drainage or road gradient.
For study and understanding, not approval of a real structure, site operation or design. Apply the correct standard, National Annex and professional review to actual engineering work.
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Sources & further reading
References open in a new tab and explain the underlying principles. The teaching text and examples here are SimpleFlick’s own; the source organisations have not endorsed this calculator.
Lesson updated: · Worked examples checked against the implemented formula; not an independent engineering certification.