No. 01 · Noon
Every formula, shown.
The formula, then a worked example with your numbers in it. Each variable and assumption is documented.
Worked example
h = s × tan θ
h = 2.77 m × tan 77° = 12.0 m
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Shadow, s17.14 m
tan θ0.7002
Height, h = s × tan θ12.0 m
Fig. 1 — Sun at 35°: the shadow measures 17.14 m, so h = s × tan θ = 17.14 m × tan 35° = 12.0 m. Open the Triangle calculator →
The working, not just the answer.
Every calculator page shows the formula, plus a worked example with your inputs substituted. Each variable and assumption is documented. No black-box math.
Change a number ↘
Triangle · height from a shadowNoon on the terrace
m
°
Height, h
h = s × tan θ
- Substituteh = 17.14 m × tan 35°
- Tangenttan 35° = 0.7002
- Multiplyh = 17.14 × 0.7002 = 12.0 m
Fig. 2 — The same triangle as the plate above. Change the shadow or the angle and the obelisk follows.
No. 02 · Afternoon
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No. 03 · Golden hour
Textbook math.
Built on math.js. Formulas come from textbooks and primary references, and each calculator documents its source and assumptions.
Source & assumptions
- Formula
- h = s · tan θ (right triangle)
- Engine
- math.js
- Assumes
- level ground, a vertical obelisk, shadow measured from its base
No. 04 · Dusk
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Fig. 8 — Night. No sun, no shadow, no triangle. The lighthouse keeps the harbour until morning.