Enter the horizontal distance and the angle (deg) into the Height From Distance Calculator. The calculator will evaluate and display the Height From Distance.
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Height Distance Formula
The calculator uses one of three formulas depending on which mode you select.
Find height (horizontal distance known):
h = d * tan(θ) + e
Find height (line-of-sight distance known):
h = s * sin(θ) + e
Find horizontal distance:
d = (H - e) / tan(θ)
Find height from two angles along the same line:
h = b * tan(α) * tan(β) / (tan(β) - tan(α)) + e
- h = total height of the target above ground
- H = known target height in distance mode
- d = horizontal distance from observer to target base
- s = line-of-sight (slope) distance to target
- θ = angle from eye level to the target (positive up, negative down)
- e = observer eye height above ground
- b = baseline, the distance moved straight toward the target between sightings
- α = angle measured from the farther position
- β = angle measured from the nearer position
The formulas assume level ground, a straight line of approach in two-angle mode, and angles strictly between -90° and 90°. Angle of elevation is positive; angle of depression is negative. The observer height is added at the end to convert eye-level rise into ground-to-top height.
Reference Tables
Use these to sanity-check inputs and results before trusting a number.
| Object | Typical height |
|---|---|
| Standard door | 2.0 m / 6.6 ft |
| One residential story | 3.0 m / 10 ft |
| Utility pole | 12 m / 40 ft |
| Mature oak tree | 20 m / 65 ft |
| Five-story building | 15 m / 50 ft |
| Cell tower | 30-60 m / 100-200 ft |
| Angle of elevation | Rise per 100 m horizontal | Rise per 100 ft horizontal |
|---|---|---|
| 5° | 8.7 m | 8.7 ft |
| 15° | 26.8 m | 26.8 ft |
| 30° | 57.7 m | 57.7 ft |
| 45° | 100 m | 100 ft |
| 60° | 173.2 m | 173.2 ft |
| 75° | 373.2 m | 373.2 ft |
Example Problems
Example 1 — Find a tree's height. You stand 25 m from the base of a tree. The angle from eye level to the top is 32°. Your eye height is 1.7 m.
Rise = 25 × tan(32°) = 15.62 m. Total height = 15.62 + 1.7 = 17.32 m.
Example 2 — Find distance to a flagpole. A flagpole is 18 m tall. From eye level (1.6 m), you measure an angle of elevation of 22° to the top.
Distance = (18 − 1.6) / tan(22°) = 16.4 / 0.4040 = 40.6 m.
Example 3 — Two-angle method. You sight the top of a building at 28°, walk 40 m straight toward it, and sight again at 48°. Eye height 1.7 m.
Rise = 40 × tan(28°) × tan(48°) / (tan(48°) − tan(28°)) = 40 × 0.5317 × 1.1106 / (1.1106 − 0.5317) = 40.81 m. Total = 42.5 m.
FAQ
Do I need to enter observer height? No. Leave it blank to get the rise above eye level only. Add it when you want the full ground-to-top height.
What if the target is below me? Enter a negative angle (angle of depression). The result will reflect a downward rise.
Why does the two-angle mode require the nearer angle to be larger? Walking toward an object always increases the angle to its top. If your nearer reading is smaller, one of the measurements is wrong or you walked away from the target.
How accurate is this? Accuracy depends on your angle measurement. A 1° error at 50 m of distance shifts the height result by roughly 0.9 m. Use a clinometer or a phone app with a stable horizon for best results.
