How long is a building's shadow? A calculator and winter table for 15 US cities

Whether a proposal casts a shadow that matters is a question for a shadow study. How far that shadow reaches is simpler, and it comes first. This page answers it for any height in any US city, with a calculator and a table for December 21, the day the sun is lowest and a date New York and San Francisco both include in their studies.

Shadow length calculator

Choose a city and a day, and type in the height. For each hour from 9am to 3pm you get the sun’s angle, the length of the shadow on level ground and the direction it points.

December 21 shadows in 15 US cities

Read each figure as a multiplier: the height of a wall or roof edge times that figure is the length of its shadow on level ground.

Download the data (CSV): every hour from 8am to 4pm on three days of the year, with the sun’s height and direction.

Latitude explains most of the spread, from Miami in the south to Seattle in the north. The clock explains the rest. New York and Philadelphia sit close to the longitude Eastern Time is set by, so their 9am and 3pm shadows come out close to each other. Boston’s shadows lengthen sooner in the afternoon, and Atlanta’s stay long later into the morning, because each sits far from that line.

How to work it out by hand

Divide the height by the tangent of the sun’s angle above the horizon. At 9am on December 21 in New York the sun stands 14.2° up, and tan(14.2°) is 0.254, so a 30-foot wall casts a shadow of 30 ÷ 0.254, or about 118 feet.

The shadow points directly away from the sun. In a US winter the sun stays in the southern sky, so a New York shadow swings from northwest at 9am, through north at noon, to northeast at 3pm.

How much the season changes it

No input moves the answer more than the date. At noon standard time in New York, a 30-foot building’s shadow is about 62 feet long on December 21 and about 9 feet on June 21, when the sun stands 73° up.

That is why the days a city tests matter so much. New York studies four days, San Francisco adds the worst-case day for the park in question, and Los Angeles counts hours of shade across two seasons. Our comparison of shadow study rules in five cities sets them side by side, Boston’s park laws included.

Where this stops and a shadow study starts

The calculator gives the length of one shadow on flat ground. A slope stretches a shadow downhill and shortens it uphill, a neighboring wall catches it, and a roof’s shape changes where its edge lands, none of which a formula knows. A real study also asks a different question: how long the shadow stays on a park, a yard or a solar panel, and when.

For that, the building has to be modeled on its site. The same model can then be rendered with the sun in its true position for that date and hour, so the rendering and the study show the same thing. Our guide to renderings for planning submissions covers what reviewers look for.

How we worked it out

The sun’s position comes from the equations behind NOAA’s Solar Calculator, based on Jean Meeus’s Astronomical Algorithms, with NOAA’s correction for atmospheric refraction. NOAA notes that it no longer maintains the calculator itself; the equations are unchanged. We checked our results against timeanddate.com’s solar noon figure for New York on December 21, 2026, which matched to the tenth of a degree and the minute.

Each city is taken at its center, on its standard time, with the figures worked for 2026. They shift only slightly from year to year. A shadow’s far edge is soft, especially with the sun low, so treat a long shadow as an estimate. If you find an error, tell us and we will check it and correct the page.

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More data and rule comparisons you can cite are on our research page. Have a project in mind? Send us the drawings and a line on what the renderings are for. You’ll have a fixed price, a written scope and a delivery date by the next business morning.