Zerdly

Vertical Difference Calculator

Computes the vertical height difference from a slope distance and vertical angle.

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How to use this calculator

Inputs

Line-of-sight height difference and horizontal distance from a slope distance and a vertical or zenith angle.

Angle
Heights for a target RL (all three, or none)

Enter the values and press Calculate.

Or load an example to see a worked result.

Your sight
Schematic
Your sightSchematic right triangle from instrument to target.vd cos vd sin vslope dinstrument
Calculate to label the triangle with your slope distance, angle and components.

Batch from CSV

One row per calculation, with a header row. Values use the units currently selected in the form above. Up to 10,000 rows; nothing is uploaded.

How the method works

Vertical angle and zenith angle
Illustrative method
Vertical angle and zenith angleA right triangle from the instrument to the target: slope distance along the hypotenuse, horizontal distance along the base, vertical difference up the far side, with the vertical angle measured from the horizontal.v = +6°horizontal 49.7261 mΔH 5.2264 mslope 50 minstrument
An elevation angle is measured up from the horizontal; a zenith angle is measured down from straight up, so v = 90° − z. A 50 m slope at +6° (zenith 84°) gives a vertical difference of 50 × sin 6° = 5.2264 m and a horizontal distance of 50 × cos 6° = 49.7261 m. Angle exaggerated for legibility.

Fixed example values for illustration — not your result.

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

  1. Enter the slope distance and choose how the angle was measured: from horizontal, or as a zenith angle.
  2. Enter the angle in DD, DMS or DDM.
  3. For a target RL, add the station RL, instrument height and target height — all three, or none.
  4. Choose the angle notation (DD, DMS, DDM or gon). Use the observation label and the batch CSV run to reduce many sights; the export carries the convention and the instrument and target heights.

How it works

Line-of-sight vertical = d × sin v and horizontal = d × |cos v|, with v measured from horizontal. A zenith angle z converts as v = 90° − z.

Target RL = station RL + instrument height + vertical − target height.

No earth-curvature or refraction correction is applied, which suits short sights.

Worked example

50 m at 6°. Vertical 5.2264 m, horizontal 49.7261 m; a zenith angle of 84° gives the same. From a station at RL 100 with HI 1.5 and target 2.0, the target is at RL 104.7264.

Common mistakes

  • Entering a zenith angle as a vertical angle (or the reverse) — 84° zenith is +6°, not 84°.
  • Forgetting the instrument and target heights when carrying an RL.
  • Applying it to long sights without a curvature and refraction correction.

Frequently asked questions

Is the angle from horizontal or vertical?

Either — choose the convention. From horizontal a downward sight is negative; a zenith angle above 90° looks down.

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Cite this tool

Zerdly. (2026). Vertical Difference Calculator. Retrieved from https://www.zerdly.com/tools/vertical-difference-calculator/

Tip: Enter any known values to calculate the remaining results.

Designed to run locally in your browser. Tool inputs are not intentionally stored by Zerdly unless stated otherwise.