---
title: "Sun Path Calculator: How Far Will That Shadow Reach in Winter?"
canonical: "https://theyieldgrid.com/sun-path-calculator/"
model_id: "tyg-863"
model_version: "1.0.0"
last_reviewed: "2026-08-20T08:02:27"
reviewed_by: "Umer Hayiat"
---

# Sun Path Calculator: How Far Will That Shadow Reach in Winter?

> Canonical calculator: [https://theyieldgrid.com/sun-path-calculator/](https://theyieldgrid.com/sun-path-calculator/)

## What this calculator does

Home - Free Gardening Calculators & Tools - Sun Path Calculator: How Far Will That Shadow Reach in Winter? Shadow length is not a fixed property of an object. It changes by season, latitude, and time of day -- and the difference between a summer shadow and a winter shadow is not small. At 45 degrees north latitude, a 20-foot house casts roughly an 8-foot shadow at solar noon in June. By December, that same house casts a shadow past 50 feet. Garden beds that get full sun in July can be in deep shade for four consecutive months without the gardener ever realizing it until the crops fail.

## Inputs

| Input | ID | Type | Unit | Range or choices | Required |
|---|---|---|---|---|---|
| Object Height (feet) | `sunang_height` | number | feet | 0.1 to 500 | No |
| Latitude (degrees) | `sunang_latitude` | number |  | 0 to 90 | No |
| Season | `sunang_season` | select |  | — Select Season — = ``; Summer Solstice (Jun 21) = `summer`; Winter Solstice (Dec 21) = `winter` | No |

## Outputs

| Output ID | Default state |
|---|---|
| `sunang_height_err` |  |
| `sunang_lat_err` |  |
| `sunang_season_err` |  |
| `sunang_results_panel` | Sun Altitude Angle — degrees above horizon ☀ Summer Shadow — feet ❄ Winter Shadow — feet Shadow Diagram H Shadow Length θ ☀ Reference: Shadow Lengths at Your Latitude Object Height ☀ Summer Shadow ❄ Winter Shadow Winter ÷ Summer How this calculator works Step 1 — Solar Declination The sun’s declination varies through the year: +23.5° at Summer Solstice (maximum north tilt), −23.5° at Winter Solstice (maximum south tilt). Declination = +23.5° (Summer) or −23.5° (Winter) Step 2 — Sun Altitude Angl |
| `sunang_out_primary` | — |
| `sunang_out_summer` | — |
| `sunang_out_winter` | — |
| `sunang_warning_area` |  |

## Formula and method

The tool uses precise trigonometry based on latitude and solstice declination to show why winter shadows are dramatically longer. Show the calculation steps Step 1: Determine solar declination. The sun's declination is the angle between the sun and Earth's equatorial plane. It reaches its maximum positive value (+23.5 degrees) at the Summer Solstice (approximately June 21) and its maximum negative value (-23.5 degrees) at the Winter Solstice (approximately December 21). This calculator uses these solstice extremes only. Declination = +23.5 degrees (Summer Solstice) or -23.5 degrees (Winter Solstice) Step 2: Calculate the sun altitude angle at solar noon. The altitude angle is how high the sun sits above the horizon at its highest point of the day. The formula: Altitude = (90 - Latitude) + Declination At 45 degrees north, Winter Solstice: (90 - 45) + (-23.5) = 21.5 degrees above the horizon. Step 3: Calculate shadow length using trigonometry. For a vertical object on flat ground at solar noon: Shadow Length = Height / tan(Altitude) The tangent function relates the angle to the ratio of object height to shadow length. As the angle approaches 90 degrees (sun directly overhead), the shadow approaches zero. As the angle approaches 0 degrees, the shadow approaches infinity. Rounding: Results are displayed to one decimal place in feet. The intermediate angle calculation retains full floating-point precision. Unit note: Height is entered in feet and output is in feet. The calculation is unit-agnostic -- entering height in meters produces shadow length in meters. Assumptions and Limits All results represent solar noon conditions only -- the moment when the sun is at its daily maximum elevation. Shadows at any other time of day are longer. The solstice dates used are June 21 (summer) and December 21 (winter). These are planning extremes; actual shadow lengths vary daily. The formula assumes the object is vertical and the ground is flat and level. Sloped terrain will alter shadow reach in ways this calculator does not model. At latitudes above approximately 66.5 degrees (the Arctic Circle), the Winter Solstice sun angle may fall at or below zero, indicating polar night. The shadow length formula does not apply in this condition; the calculator flags this case. Solar declination is simplified to exactly +/-23.5 degrees for solstice dates. The actual value is approximately 23.44 degrees, introducing a rounding difference of less than 0.1 degree. The calculator does not account for atmospheric refraction, which can make the sun appear slightly higher than its geometric position suggests. This effect is most significant near the horizon (low winter angles) and can add roughly 0.5 to 1 degree in apparent altitude. Surrounding objects, topography, and tree canopy are not modeled. The shadow calculated is for a single isolated object.

## Verified worked examples

### Example 1: 20-foot house at 45 degrees north latitude

Object Height: 20 ft Latitude: 45 degrees Summer Solstice sun angle: (90 - 45) + 23.5 = 68.5 degrees Winter Solstice sun angle: (90 - 45) - 23.5 = 21.5 degrees Result: Summer shadow = 20 / tan(68.5°) = 7.9 ft. Winter shadow = 20 / tan(21.5°) = 50.8 ft. A garden bed placed 15 feet north of this house sits outside its summer shadow entirely -- but in nearly full winter shade. Any winter greens, cold frames, or overwintering crops within 50 feet need supplemental light or relocation.

### Example 2: 40-foot oak tree at 35 degrees north latitude

Object Height: 40 ft Latitude: 35 degrees Summer Solstice sun angle: (90 - 35) + 23.5 = 78.5 degrees Winter Solstice sun angle: (90 - 35) - 23.5 = 31.5 degrees Result: Summer shadow = 40 / tan(78.5°) = 8.1 ft. Winter shadow = 40 / tan(31.5°) = 65.3 ft. Even at the relatively sunny 35-degree latitude, a mature tree creates a 65-foot shadow corridor in December. Any bed within that radius that is being used for winter gardening will receive little to no direct midday sun.

### Example 3: 6-foot wooden fence at 55 degrees north latitude

Object Height: 6 ft Latitude: 55 degrees (central UK, northern Germany, southern Canada) Summer Solstice sun angle: (90 - 55) + 23.5 = 58.5 degrees Winter Solstice sun angle: (90 - 55) - 23.5 = 11.5 degrees Result: Summer shadow = 6 / tan(58.5°) = 3.7 ft. Winter shadow = 6 / tan(11.5°) = 29.5 ft. A standard garden fence that barely shades anything in summer creates a shadow nearly the length of a full allotment bed in winter. At high latitudes, even low structures like cold frames, compost bins, or trellises deserve a winter shadow check.

## Assumptions

The tool uses precise trigonometry based on latitude and solstice declination to show why winter shadows are dramatically longer. Show the calculation steps Step 1: Determine solar declination. The sun's declination is the angle between the sun and Earth's equatorial plane. It reaches its maximum positive value (+23.5 degrees) at the Summer Solstice (approximately June 21) and its maximum negative value (-23.5 degrees) at the Winter Solstice (approximately December 21). This calculator uses these solstice extremes only. Declination = +23.5 degrees (Summer Solstice) or -23.5 degrees (Winter Solstice) Step 2: Calculate the sun altitude angle at solar noon. The altitude angle is how high the sun sits above the horizon at its highest point of the day. The formula: Altitude = (90 - Latitude) + Declination At 45 degrees north, Winter Solstice: (90 - 45) + (-23.5) = 21.5 degrees above the horizon. Step 3: Calculate shadow length using trigonometry. For a vertical object on flat ground at solar noon: Shadow Length = Height / tan(Altitude) The tangent function relates the angle to the ratio of object height to shadow length. As the angle approaches 90 degrees (sun directly overhead), the shadow approaches zero. As the angle approaches 0 degrees, the shadow approaches infinity. Rounding: Results are displayed to one decimal place in feet. The intermediate angle calculation retains full floating-point precision. Unit note: Height is entered in feet and output is in feet. The calculation is unit-agnostic -- entering height in meters produces shadow length in meters. Assumptions and Limits All results represent solar noon conditions only -- the moment when the sun is at its daily maximum elevation. Shadows at any other time of day are longer. The solstice dates used are June 21 (summer) and December 21 (winter). These are planning extremes; actual shadow lengths vary daily. The formula assumes the object is vertical and the ground is flat and level. Sloped terrain will alter shadow reach in ways this calculator does not model. At latitudes above approximately 66.5 degrees (the Arctic Circle), the Winter Solstice sun angle may fall at or below zero, indicating polar night. The shadow length formula does not apply in this condition; the calculator flags this case. Solar declination is simplified to exactly +/-23.5 degrees for solstice dates. The actual value is approximately 23.44 degrees, introducing a rounding difference of less than 0.1 degree. The calculator does not account for atmospheric refraction, which can make the sun appear slightly higher than its geometric position suggests. This effect is most significant near the horizon (low winter angles) and can add roughly 0.5 to 1 degree in apparent altitude. Surrounding objects, topography, and tree canopy are not modeled. The shadow calculated is for a single isolated object. All results represent solar noon conditions only -- the moment when the sun is at its daily maximum elevation. Shadows at any other time of day are longer. The solstice dates used are June 21 (summer) and December 21 (winter). These are planning extremes; actual shadow lengths vary daily. The formula assumes the object is vertical and the ground is flat and level. Sloped terrain will alter shadow reach in ways this calculator does not model. At latitudes above approximately 66.5 degrees (the Arctic Circle), the Winter Solstice sun angle may fall at or below zero, indicating polar night. The shadow length formula does not apply in this condition; the calculator flags this case. Solar declination is simplified to exactly +/-23.5 degrees for solstice dates. The actual value is approximately 23.44 degrees, introducing a rounding difference of less than 0.1 degree. The calculator does not account for atmospheric refraction, which can make the sun appear slightly higher than its geometric position suggests. This effect is most significant near the horizon (low winter angles) and can add roughly 0.5 to 1 degree in apparent altitude. Surrounding objects, topography, and tree canopy are not modeled. The shadow calculated is for a single isolated object. The core value of a sun angle and shadow calculator is not the summer result -- it is the winter result. Most gardening shade decisions are made in summer, when everything looks bright and promising. The critical check is: what happens in December? Critical Warnings: The summer shadow is not representative. At 45 degrees north latitude, winter shadows are typically 6 to 7 times longer than summer shadows for the same object. A tree that barely shades anything in July may cast a shadow well past your furthest raised bed in January. Polar and near-polar conditions invalidate the formula. Above 66.5 degrees north latitude, the Winter Solstice sun angle drops below zero degrees, meaning the sun does not rise above the horizon. Shadow length becomes undefined -- not very long, but nonexistent. Gardeners at high latitudes relying only on summer shade analysis are missing this entirely. Solar noon is not representative of all-day light. This calculator gives you the minimum shadow length for the day (at solar noon). In the early morning and late afternoon, even in summer, shadows from the same object extend far longer. For beds used in shoulder seasons, account for the full arc. Structures grow. A 10-foot shrub planted near a garden today may be a 25-foot shrub in five years. Factor in expected mature height, not current height, when making permanent bed placement decisions. Minimum Standards for Garden Bed Placement: Place vegetable beds at least as far from any structure as the structure's winter shadow length, measured from the north-facing side. This ensures they clear the maximum midday shadow of the year. For year-round production beds, the clearance buffer should be the full winter shadow length plus an additional margin for morning and afternoon shadow sweep. Competitor Trap: Many online shadow calculators and articles provide only a static shadow length for "typical" conditions without specifying the solar angle assumptions or whether the result is a solstice extreme or an equinox midpoint. This makes the output look precise while being operationally useless for planning: a gardener who does not know whether they are looking at a June 21 noon figure or an October 15 average figure cannot make a reliable bed-placement decision. A sun path calculator that does not expose its solstice versus equinox assumptions is answering the wrong question. If you are also evaluating your garden's capacity after determining sun exposure, the square foot gardening planner integrates well as a next layer of spatial planning. For gardeners working with chill-dependent crops in shaded microclimates, the chill hours calculator can help quantify winter cold accumulation in those areas.

## Limitations and safety

All results represent solar noon conditions only -- the moment when the sun is at its daily maximum elevation. Shadows at any other time of day are longer. The solstice dates used are June 21 (summer) and December 21 (winter). These are planning extremes; actual shadow lengths vary daily. The formula assumes the object is vertical and the ground is flat and level. Sloped terrain will alter shadow reach in ways this calculator does not model. At latitudes above approximately 66.5 degrees (the Arctic Circle), the Winter Solstice sun angle may fall at or below zero, indicating polar night. The shadow length formula does not apply in this condition; the calculator flags this case. Solar declination is simplified to exactly +/-23.5 degrees for solstice dates. The actual value is approximately 23.44 degrees, introducing a rounding difference of less than 0.1 degree. The calculator does not account for atmospheric refraction, which can make the sun appear slightly higher than its geometric position suggests. This effect is most significant near the horizon (low winter angles) and can add roughly 0.5 to 1 degree in apparent altitude. Surrounding objects, topography, and tree canopy are not modeled. The shadow calculated is for a single isolated object. The core value of a sun angle and shadow calculator is not the summer result -- it is the winter result. Most gardening shade decisions are made in summer, when everything looks bright and promising. The critical check is: what happens in December? Critical Warnings: The summer shadow is not representative. At 45 degrees north latitude, winter shadows are typically 6 to 7 times longer than summer shadows for the same object. A tree that barely shades anything in July may cast a shadow well past your furthest raised bed in January. Polar and near-polar conditions invalidate the formula. Above 66.5 degrees north latitude, the Winter Solstice sun angle drops below zero degrees, meaning the sun does not rise above the horizon. Shadow length becomes undefined -- not very long, but nonexistent. Gardeners at high latitudes relying only on summer shade analysis are missing this entirely. Solar noon is not representative of all-day light. This calculator gives you the minimum shadow length for the day (at solar noon). In the early morning and late afternoon, even in summer, shadows from the same object extend far longer. For beds used in shoulder seasons, account for the full arc. Structures grow. A 10-foot shrub planted near a garden today may be a 25-foot shrub in five years. Factor in expected mature height, not current height, when making permanent bed placement decisions. Minimum Standards for Garden Bed Placement: Place vegetable beds at least as far from any structure as the structure's winter shadow length, measured from the north-facing side. This ensures they clear the maximum midday shadow of the year. For year-round production beds, the clearance buffer should be the full winter shadow length plus an additional margin for morning and afternoon shadow sweep. Competitor Trap: Many online shadow calculators and articles provide only a static shadow length for "typical" conditions without specifying the solar angle assumptions or whether the result is a solstice extreme or an equinox midpoint. This makes the output look precise while being operationally useless for planning: a gardener who does not know whether they are looking at a June 21 noon figure or an October 15 average figure cannot make a reliable bed-placement decision. A sun path calculator that does not expose its solstice versus equinox assumptions is answering the wrong question. If you are also evaluating your garden's capacity after determining sun exposure, the square foot gardening planner integrates well as a next layer of spatial planning. For gardeners working with chill-dependent crops in shaded microclimates, the chill hours calculator can help quantify winter cold accumulation in those areas.

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## Provenance

- Model ID: `tyg-863`
- Model version: `1.0.0`
- Reviewed by: Umer Hayiat
- Page modified: 2026-08-20T08:02:27
- Runtime SHA-256: `51c745e832cdd0856de8066e82338534ebd103b5578e1e6f86a690686040b8eb`

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