Assumes a vertical object on level ground and ignores atmospheric refraction, so results near sunrise and sunset are approximate.
Formula and breakdown
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This shadow length calculator works out how long a shadow will be from an object's height and the sun's angle, or from a date, clock time and place in the UK, Ireland or Europe, and it can also turn a measured shadow back into the sun's angle. Gardeners, builders, solar installers and anyone planning a fence, extension or panel array can use it to see where shade will fall and how far it will reach.
Quick answer: A shadow length calculator divides an object's height by the tangent of the sun's elevation angle. A 1.8 m fence with the sun 15 degrees high, typical of London at noon in late December, casts a 6.7 m shadow. At 45 degrees the shadow equals the height, and at lower angles it is longer.
What Is a Shadow Length Calculator?
A shadow length calculator is a tool that finds the length of the shadow cast by a vertical object on level ground from the object's height and the sun's elevation above the horizon. In plain words: shadow length equals height divided by the tangent of the sun's elevation angle, and the shadow points directly away from the sun.
The height, the shadow and the sun's ray form a right-angled triangle. The sun's elevation is the angle between the ray and the ground, and it is the complement of the solar zenith angle described in the Wikipedia article on the solar zenith angle. When you only know the date, time and place, the shadow length calculator first works out the sun's elevation and direction, then applies the same triangle.
How Do You Use the Shadow Length Calculator?
- Pick what you know: the sun's elevation, the date, time and place, or a shadow you have measured.
- Enter the object's height and choose metres or feet.
- For the sun elevation mode, type the angle in degrees above the horizon.
- For the date mode, choose a city or enter your own latitude and longitude, then set the date, the clock time and the clock's offset from UTC (0 for UK winter time, 1 for British Summer Time).
- For the measured shadow mode, enter the shadow length on level ground to get the sun's elevation.
- Read the shadow length, the shadow to height ratio, the shadow direction and the time and length of the shortest shadow of the day. Open the formula panel to see each step.
How Do You Calculate the Length of a Shadow?
Divide the object's height by the tangent of the sun's elevation: a 3 m pole with the sun at 30 degrees casts 3 / tan(30) = 3 / 0.577 = 5.2 m. A useful check is 45 degrees, where tan equals 1 and the shadow is exactly as long as the object is tall. Above 45 degrees the shadow is shorter than the height; below it, longer, and the growth is steep near the horizon.
The table shows the shadow to height ratio for common sun angles. Multiply the ratio by any height to get the shadow length in the same unit.
| Sun elevation | Shadow to height ratio | Shadow of a 1.8 m fence |
|---|---|---|
| 5 degrees | 11.43 | 20.6 m |
| 10 degrees | 5.67 | 10.2 m |
| 15 degrees | 3.73 | 6.7 m |
| 20 degrees | 2.75 | 4.9 m |
| 30 degrees | 1.73 | 3.1 m |
| 45 degrees | 1.00 | 1.8 m |
| 60 degrees | 0.58 | 1.0 m |
How Do You Work Out the Sun's Angle for a Date and Place?
The sun's elevation depends on latitude, the date (which sets the sun's declination, from about minus 23.4 degrees in late December to plus 23.4 degrees in late June) and the time of day. The shadow length calculator uses the method published by the NOAA Global Monitoring Laboratory: it finds the declination and the equation of time from the day of the year, converts clock time to true solar time using longitude and the UTC offset, and then gets the zenith angle from cos(zenith) = sin(latitude) sin(declination) + cos(latitude) cos(declination) cos(hour angle).
Clock time matters. Solar noon, when shadows are shortest and point due north in the UK, falls a few minutes either side of 12:00 GMT in London in winter, but around 13:00 during British Summer Time, and later still in western places such as Cardiff and Dublin. Enter the offset that your clock actually uses on that date.
How Long Are Shadows in the UK and Europe in Winter?
At noon on the winter solstice a shadow in London is about 3.7 times the object's height, and in Aberdeen about 6 times. At the equinoxes the noon ratio in London falls to about 1.3, and at the summer solstice to about 0.53. The table gives noon values worked out from latitude and declination (noon elevation = 90 minus the difference between latitude and declination), ignoring refraction.
| City (latitude) | 21 Dec noon elevation | 21 Dec ratio | Equinox noon elevation | Equinox ratio | 21 Jun noon elevation | 21 Jun ratio |
|---|---|---|---|---|---|---|
| Aberdeen (57.2 N) | 9.4 | 6.02 | 32.8 | 1.55 | 56.3 | 0.67 |
| Edinburgh (56.0 N) | 10.6 | 5.33 | 34.0 | 1.48 | 57.5 | 0.64 |
| Dublin (53.4 N) | 13.2 | 4.25 | 36.6 | 1.35 | 60.1 | 0.57 |
| Manchester (53.5 N) | 13.1 | 4.30 | 36.5 | 1.35 | 60.0 | 0.58 |
| Berlin (52.5 N) | 14.1 | 3.99 | 37.4 | 1.31 | 60.9 | 0.56 |
| Amsterdam (52.4 N) | 14.2 | 3.95 | 37.6 | 1.30 | 61.1 | 0.55 |
| London (51.5 N) | 15.1 | 3.71 | 38.4 | 1.26 | 61.9 | 0.53 |
| Paris (48.9 N) | 17.7 | 3.13 | 41.1 | 1.15 | 64.6 | 0.48 |
| Rome (41.9 N) | 24.7 | 2.18 | 48.0 | 0.90 | 71.6 | 0.33 |
| Madrid (40.4 N) | 26.2 | 2.04 | 49.5 | 0.85 | 73.0 | 0.31 |
Elevations are in degrees. Noon is the shortest shadow of the day; morning and afternoon shadows are longer.
Why Does Shadow Length Matter for Solar Panels?
A shadow that reaches a solar panel cuts its output, so the winter noon ratio is a practical rule for spacing: an obstacle about 2 m taller than your panels, south of them in London, throws shade about 7.4 m north at noon in late December. Panels are usually tilted towards the low winter sun, and the solar panel angle calculator shows the best tilt for your latitude. If shade from a tree or chimney is unavoidable, a different direction may help, which you can compare with the solar panel orientation calculator.
The same triangle explains row spacing on flat roofs: the raised back edge of a tilted panel casts a shadow on the row behind. The solar row spacing calculator applies this to panel rows, and the roof area calculator shows how many panels fit once gaps are allowed for.
How Do You Find the Sun's Angle From a Shadow?
Take the arctangent of height divided by shadow length: a 2 m post with a 4 m shadow means the sun is arctan(0.5) = 26.6 degrees above the horizon. Measure on flat, level ground with the object upright, and measure to the middle of the soft edge at the tip of the shadow. The measured shadow mode does this calculation for you.
Worked Example: How Far Does a Garden Fence Shade a Lawn in December?
Example: a household in Manchester has a 1.8 m fence running east to west along the south side of the garden and wants to know how much of the lawn stays in shade at midday on 21 December.
- Choose Manchester, date 21 December, clock offset 0 (GMT).
- Solar noon in Manchester is a little after 12:00 GMT, because Manchester lies about 2.2 degrees west of Greenwich, which delays solar noon by about 9 minutes before the equation of time is applied.
- Noon sun elevation: 90 minus (53.48 + 23.42) = 13.1 degrees.
- Shadow: 1.8 / tan(13.1) = 1.8 / 0.233 = 7.7 m.
- At the equinox the noon sun reaches about 36.5 degrees, and the shadow shrinks to 1.8 / 0.740 = 2.4 m.
So in midwinter the first 7.7 m of lawn north of the fence stays in shade all day, which matters when placing a vegetable bed, a greenhouse or a ground-mounted panel.
Frequently Asked Questions
What is the formula for shadow length?
Shadow length equals object height divided by the tangent of the sun's elevation angle above the horizon. A 3 m pole with the sun at 30 degrees casts 3 / 0.577 = 5.2 m. The formula assumes a vertical object standing on level ground.
How do I find the sun's angle from a shadow?
Measure the object's height and its shadow on level ground, then take the arctangent of height divided by shadow. A 2 m post with a 2 m shadow means the sun is 45 degrees high; a 4 m shadow means about 26.6 degrees.
When is a shadow the shortest?
A shadow is shortest at solar noon, when the sun is highest for that day and due south in the UK and Europe. Solar noon is rarely at 12:00 on the clock: in London it falls around 13:00 in summer because of British Summer Time.
Why are shadows so long in winter?
In winter the sun stays low. In London the noon sun reaches only about 15 degrees at the winter solstice, so a shadow is about 3.7 times the object's height, compared with about 0.53 times at the summer solstice, when the sun reaches about 62 degrees.
Which way does a shadow point?
A shadow always points directly away from the sun. In the UK the morning sun is in the east to south-east, so shadows fall west to north-west; at solar noon they point due north; in the evening they fall towards the east.
How accurate is a shadow length calculator?
For a vertical object on level ground the published NOAA equations give the sun angle closely enough for gardens, building and solar planning. Errors grow when the sun is under about 5 degrees, because refraction lifts the sun's image and shadow edges become blurred.
Checked October 2026 by the Solaxyra Editorial Team. Sources: NOAA Global Monitoring Laboratory: General Solar Position Calculations, Wikipedia: Solar zenith angle.