Slope & Horizontal Distance Calculator
Converts between slope and horizontal distance using the vertical angle or height difference.
Enter any two
Fill exactly two fields — the rest are solved. Angles accept and display in DD, DMS or DDM. Runs in your browser.
Triangle
slope² = horizontal² + ΔH²; tan(angle) = ΔH ÷ horizontal; zenith = 90° − angle.
Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.
How to use this calculator
- Pick your angle format (DD, DMS or DDM) at the top — it sets how the angle is read and shown.
- Enter any TWO of: slope distance, horizontal distance, height difference ΔH and the vertical angle (from horizontal).
- Read the solved sides plus the zenith angle, grade % and 1:N ratio, with a scaled triangle diagram. It works both ways (slope → horizontal and horizontal → slope).
How it works
Slope, horizontal and the height difference form a right triangle: slope² = horizontal² + ΔH², with tan(vertical angle) = ΔH ÷ horizontal.
Given any two of the four quantities the tool solves the other two, then derives the zenith angle (90° − vertical angle), the grade (ΔH ÷ horizontal × 100%) and the run-per-rise ratio (1:N). Angles can be entered and read in DD, DMS or DDM.
Worked example
Slope 100 m at 5°. Horizontal ≈ 99.619 m, ΔH ≈ 8.716 m, zenith 85°, grade ≈ 8.749% (about 1:11.43).
Common mistakes
- Mixing up the vertical angle (from horizontal) with the zenith angle (from vertical) — they add to 90°.
- Entering three or four values — fill exactly two and the rest are solved.
- Reading the grade as the angle — grade is the tangent of the angle as a percentage, not the angle itself.
Frequently asked questions
Why reduce slope to horizontal (and back)?
Plans and grids use horizontal distance, but a tape or EDM measures along the slope, which is longer. Set-out often needs the reverse — the slope distance to mark out for a known horizontal and grade.
What is the zenith angle?
The angle measured from vertical (straight up) rather than from horizontal. Total stations often read zenith angles; it equals 90° minus the vertical angle.
How do I get the grade or 1:N ratio?
The tool shows both: grade % = ΔH ÷ horizontal × 100, and the ratio 1:N where N = horizontal ÷ ΔH (run per unit rise).
What if I enter three or four values?
Enter exactly two. With more than two the inputs could disagree, so the tool asks you to leave two blank.
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Cite this tool
Zerdly. (2026). Slope & Horizontal Distance Calculator. Retrieved from https://www.zerdly.com/tools/horizontal-distance-from-slope-distance-calculator/
Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.