About the Tree Canopy Shade Calculator
The Tree Canopy Shade Calculator computes shadow length and shaded area cast by a tree at solar noon for a given latitude and season. It applies the standard solar-altitude formula (angle = 90° − latitude + solar declination, where declination ranges from −23.5° at winter solstice to +23.5° at summer solstice) and uses simple trigonometry to project shadow length from tree height. Canopy width determines total shaded ground area.
It is built for homeowners planting shade trees for west/southwest summer cooling, garden designers placing sun-tolerant vs shade-tolerant plants, solar-panel shoppers stress-testing whether neighbor trees will shade panels in winter (the killer scenario), arborists explaining canopy impact to clients, and anyone planning a patio location and wondering whether the existing oak will shade it at 3 PM in July.
All calculations run locally in JavaScript. Tree dimensions, latitude, and season inputs never leave your device. The page makes no network call after first load. Solar-azimuth lookup tables are bundled into the JavaScript on initial load.
For maximum residential cooling, plant large-canopy deciduous trees 15–20 ft west or southwest of the house to block summer afternoon sun (12–6 PM, June–August), then let leaves drop and let winter sun reach the building for passive solar heating. Deciduous trees block ~90% of summer sun in full leaf and 50–70% of winter sun — evergreens block sun year-round, which often increases winter heating costs and makes the house feel gloomy in short winter days. Don’t plant within 20 ft of foundation; root damage offsets the cooling benefit.
How to Use the Canopy Shade Calculator
Enter the tree’s height and mature canopy width. Pick your latitude from the dropdown (the closer you are to the equator, the shorter the shadows). Choose a season, and the calculator uses the sun’s actual altitude angle on that date at solar noon to work out exactly how far the tree’s shadow falls and how much ground area it covers. Toggle between the four seasons to see how dramatically shadows change across the year.
The Math Behind the Shadow
The calculation starts with the sun’s solar altitude angle — the angle between the horizon and the sun. At solar noon, this angle is given by altitude = 90° – latitude + declination, where declination is the sun’s position relative to the equator (+23.45° at summer solstice, –23.45° at winter solstice, 0° at the equinoxes).
Shadow length is then simply height / tan(altitude). So a 40-foot tree at 40°N latitude on the summer solstice has a sun altitude of 73.45°, producing a noon shadow of about 12 feet. The same tree on the winter solstice has a sun altitude of only 26.55°, producing a noon shadow of roughly 80 feet — nearly 7 times longer. This is why deciduous trees are perfect for south-facing homes: dense summer shade when you need it, and a long low winter sun slipping through bare branches to warm the house when you want it.
Strategic Placement for Energy Savings
The U.S. Department of Energy estimates that three well-placed shade trees can save a homeowner $100–$250 per year in cooling costs, with full savings realized when the canopy matures in 10–20 years. The placement rules that maximize savings:
- West and southwest walls take the worst summer heat beating. Plant deciduous shade trees 15–20 feet from these walls. At that distance a mature 40-foot canopy will shade most of the wall and roof edge during the hottest afternoon hours.
- Never plant evergreens south of the house in heating climates. They block the low winter sun that provides free heating, costing you more in heating than you save in cooling.
- East side trees shade morning heat and are a lower priority than west-side trees but still helpful for east-facing bedrooms and kitchens.
- North side trees provide windbreak benefits in cold climates but virtually no shade value. Evergreens work best here as winter wind screens.
- Over air conditioner compressors: a shade tree that cools the AC unit by 10°F can improve its efficiency by up to 10%. Leave at least 3 feet of clearance for airflow.
The Garden Planner’s Perspective
Shadows also define what you can grow where. A spot that gets 6+ hours of direct sun between 10 AM and 4 PM is full sun — enough for tomatoes, peppers, squash, and most flowers. A spot with 4–6 hours is partial sun, best for leafy greens, herbs, and root crops. Less than 4 hours is shade, where only shade-tolerant plants like hostas, ferns, astilbe, and impatiens will thrive.
Use this calculator to plot which corner of your yard falls into which category at different seasons. A bed that’s in full sun at the spring equinox might be heavily shaded by midsummer once a large nearby tree has leafed out. Planning around this prevents the common mistake of planting tomatoes in April sun and watching them get choked out by canopy shade in July.
Why Morning and Afternoon Shadows Are Longer
The hero result shows the shortest shadow of the day, cast at solar noon when the sun is highest. Shadows at 9 AM and 3 PM are significantly longer because the sun is lower in the sky. At sunrise and sunset, shadows stretch to infinity as the sun crosses the horizon. The Pro hourly shade map walks through the full day, showing how the shadow sweeps from west (morning) through north (midday, in the northern hemisphere) to east (afternoon) — this sweep is what determines whether a specific spot in your yard gets any usable sun at all.
Latitude Matters More Than You Think
A tree in Miami (25°N) casts a dramatically shorter noon shadow at any time of year than the same tree in Minneapolis (45°N). At summer solstice in Miami, the sun is nearly overhead at 88°, so a 40-foot tree casts a noon shadow of barely 1.4 feet. In Minneapolis the same tree on the same day casts a shadow of about 15 feet. In winter the contrast is even more extreme: Miami’s winter noon sun is still at 41°, giving a 46-foot shadow — while Minneapolis’s winter noon sun is at only 22°, giving a 100-foot shadow. This is why you can get away with planting a tree much closer to a south-facing window in Florida than you can in the upper Midwest.
Planning the rest of your tree care? Use the Tree Watering Calculator to figure out how much water your shade tree needs each week, or check the Tree Pruning Calendar to know when to shape it.
Frequently Asked Questions
How much can a shade tree reduce cooling costs?
A strategically placed shade tree can cut summer cooling costs 20 to 30 percent. A mature tree casting shade on west and southwest walls during peak afternoon hours (12 to 6 PM June through August) can save 100 to 400 dollars per summer depending on climate and electricity rates.
Where should I plant a shade tree?
For maximum cooling, plant large shade trees 15 to 20 feet from the west and southwest sides of the house. This blocks brutal afternoon sun but allows winter southern sun to reach the building for passive heating. Avoid planting within 20 feet of foundation to prevent root damage.
How does latitude affect shadow length?
The farther from the equator, the lower the sun's angle and the longer the shadow. At noon on the summer solstice, a 30-foot tree casts a 2-foot shadow in Miami (25 N) but a 15-foot shadow in Seattle (47 N). In winter, shadows triple or quadruple in length across the US.
What's the difference between canopy shade and footprint shade?
Canopy shade is the area directly under the tree, equal to the canopy's horizontal spread. Footprint shade extends beyond the canopy in the direction of the shadow - this is the total area that experiences shade at a given moment. A 40-foot tree with a 30-foot canopy at 40 N in summer casts about 70 feet of total shaded area.
Do deciduous trees provide better cooling than evergreens?
Usually yes in cold and temperate climates. Deciduous trees block 90 percent of summer sun when leafed out, then drop their leaves and allow 50 to 70 percent of winter sun through for passive heating. Evergreens block sun year-round, which increases winter heating costs and can make the house feel gloomy in short winter days.
