Shadow Length Calculator
How long a shadow anything casts at any time and place — height ÷ tan(sun elevation), with the direction it falls and the solar-design uses.
The design-critical case is the winter-solstice morning: the year's longest working-hours shadows. Solar farms space rows by it (the standard rule: no inter-row shading 9 am–3 pm on Dec 21 / Jun 21 south), and the 45° moment — shadow equals height — is how Thales measured the pyramids.
Formula
⚠️ Ephemeris approximations (±1–3 min for sun times at mid-latitudes, ±0.5 day moon age) — ideal for planning; for precise almanac work use USNO/IMCCE data.
How long a shadow anything casts at any time and place — height ÷ tan(sun elevation), with the direction it falls and the solar-design uses.
About Shadow Length Calculator
A shadow is trigonometry you can stand in: object height divided by the tangent of the sun's elevation, falling exactly opposite the sun's azimuth. This calculator computes both — length and direction — for any object, place, date and clock time, which turns out to be the working math of solar-farm row spacing, building shadow studies, garden planning, sundials and the occasional pyramid measurement.
How to use Shadow Length Calculator
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula shadow = height / tan(sun elevation); direction = solar azimuth + 180° substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use Shadow Length Calculator?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula shadow = height / tan(sun elevation); direction = solar azimuth + 180° with sources cited on the page
- ✓The design-critical case is the winter-solstice morning: the year's longest working-hours shadows. Solar farms space rows by it (the standard rule: no inter-row shading 9 am–3 pm on Dec 21 / Jun 21 south), and the 45° moment — shadow equals height — is how Thales measured the pyramids.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
How do solar farms use shadow math for row spacing?+
The canonical rule: rows must not shade each other between 9 am and 3 pm SOLAR time on the winter solstice — the day-window carrying ~80% of winter energy. Compute the sun's elevation and azimuth at 9 am on Dec 21 (this tool), take the panel's top-edge height above the row's base, and the required gap is height ÷ tan(elevation) projected onto the row-spacing axis (multiply by cos of the azimuth-from-south angle). At 35° latitude that yields roughly 2.2–2.6× panel height; at 50° it blows out to 4×+, which is why high-latitude farms tilt flatter and accept some winter shading as cheaper than land.
When does a shadow equal the object's height?+
At sun elevation exactly 45° — tan(45°) = 1 — the angle Thales allegedly waited for to read the Great Pyramid's height off its shadow. When the elevation is 26.6°, shadows are 2× height; at 18.4°, 3×; near sunrise/sunset they stretch toward infinity (and go fuzzy: the sun's half-degree disc makes the penumbra grow with distance — a 100-m shadow's edge is blurred by ~1 m, the practical limit of shadow-based measurement).
Can I measure a building's height from its shadow?+
The classic method, made rigorous: measure the shadow at a noted clock time, get the sun's elevation from this tool for that exact time and location, then height = shadow × tan(elevation). Error sources to respect: sloped ground (measure along the horizontal, or correct by the grade), finding the TRUE shadow tip of a complex roofline, and timing (elevation changes ~0.2°/min at mid-morning — a 5-minute timestamp error shifts a 50-m result by a metre). Same-day calibration against an object of known height cancels most systematic error.
Why are winter shadows so dramatically long?+
Noon elevation = 90° − latitude + declination, and December's declination is −23.4°: New York's noon sun sits at just 26° (shadows 2× height at the day's BEST), London's at 15° (3.7×), and the morning/afternoon hours are far worse. The practical fallout: a 2-storey extension that's harmless in June can bury a neighbor's garden from October to February — why planning authorities demand solstice shadow diagrams, and why 'south-facing garden' premiums are really low-winter-sun-angle premiums.
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