Passive Solar Overhang Projection Calculator
Introduction: why passive solar overhang sizing matters
Passive solar overhang sizing turns a climate question into a geometry question. Instead of guessing how deep an eave should be, you can measure the window, choose the design-day sun angle, and let the calculator estimate the projection needed to keep direct summer sun off the glass. That is useful for comfort, glare control, and cooling load reduction, but it is also useful because the answer is sensitive to small changes in latitude and sun position. A detail that looks modest on paper can materially change how much of the opening gets shade at noon.
This calculator focuses on one fixed horizontal overhang and one chosen design day. That is deliberate. A simple first-pass sizing tool is often the fastest way to compare roof ideas, evaluate retrofit options, or test whether a proposed fascia depth is likely to work before anyone sketches the full facade. The result is not a year-round sun study; it is a targeted shading length that helps you see whether the geometry is in the right range.
The sections below explain how to enter the site data, what the formula is doing, how the default values behave, and which assumptions matter when you move from a calculator result to a real building detail. The examples are about passive solar overhangs specifically, so every quantity refers to the same shadow triangle: latitude sets the noon sun angle, window height sets the shaded vertical span, and the offset adds the clearance between the top of the glazing and the underside of the overhang.
What this calculator solves for passive-solar shade design
The question being answered is narrow and practical: for a horizontal overhang above a window, how far must the projection extend to shade a chosen vertical portion of glass at solar noon on the design day? The calculator does not try to guess the best architecture, and it does not optimize for the whole year. It solves the shadow-triangle problem you would otherwise work through with a pencil, a site latitude, and a tangent table.
That makes it especially useful when you are deciding between several rough dimensions. If one proposal already comes close, you can test whether a slightly deeper soffit, a higher mounting point, or a different design-day declination gives a better fit. Because the computation depends on both the sun angle and the visible window geometry, the answer changes in a way that is easy to reason about: a higher sun means less projection, while a lower sun or a larger shaded height means more projection.
How to use this calculator for passive-solar overhangs
To size a passive-solar overhang, enter the geometric inputs that define the shadow triangle and let the page calculate the resulting projection length. The calculator is intentionally simple, so each input has one job and one job only.
- Latitude (°) sets the site location that controls the noon sun angle.
- Window Height to Shade (m) is the vertical portion of glass you want protected from direct sun.
- Overhang Height Above Window Top (m) is the vertical gap between the top of the window and the underside of the overhang.
- Design Day Declination (°) represents the sun position you want to design around.
- Submit the form to update the result box with the calculated projection.
- Compare the output against the actual roof, fascia, or balcony depth you can build.
If you are checking more than one facade, keep each set of inputs together. Passive solar design is easiest to evaluate when latitude, opening height, and offset are recorded as a complete package rather than as isolated numbers. That way, when you return to the design later, you can tell whether a deeper overhang is the result of a location change, a window change, or simply a different declination target.
Inputs: how to pick good values for overhang sizing
The inputs should describe the real opening you are trying to shade, not an idealized version of it. Measure the window height to the area that actually needs protection, and measure the offset from the top of the glazing to the underside of the overhang you intend to use. If the project is still conceptual, estimate carefully and be explicit about the assumptions so that later revisions are easy to spot.
- Latitude (°): use the latitude of the facade or the nearest representative site location.
- Window Height to Shade (m): use the height of the glass that needs the most direct-sun protection.
- Overhang Height Above Window Top (m): measure the vertical distance from the window head to the underside of the shade.
- Design Day Declination (°): choose the declination that matches your design intent, whether that is a peak summer date or another target condition.
The prefilled values are a starting point, not a recommendation. They show a plausible passive-solar case so you can see how the result changes, but they should be replaced with project-specific data before you rely on the answer. If one input is uncertain, test a tighter version and a looser version to see whether the required projection stays within the architectural limits you have available.
Passive solar overhang formula: from sun angle to projection
For a fixed horizontal overhang, the calculation begins with the solar altitude at noon. That altitude determines the angle of the shadow ray, and the shadow ray determines how much horizontal distance is needed to cover the selected vertical span of window. The relation is straightforward: a higher sun produces a shorter shadow and a smaller projection, while a lower sun forces the overhang to reach farther.
Once the altitude is known, the calculator adds the vertical gap above the window to the height of glass being shaded and uses that combined distance as the target height for the shadow triangle.
The projection then comes from the tangent of the solar altitude.
Another way to read the same relationship is from the ratio of the vertical and horizontal sides of the triangle.
Here, φ is latitude, δ is declination, H is the window height to shade, O is the overhang offset above the window, S is the total vertical span the shade must cover, and L is the horizontal projection length. The calculator follows this relationship every time the inputs change.
Worked example: default passive-solar overhang sizing at 40° latitude
Using the default values on the page, the solar altitude at noon is easy to check by hand. With latitude 40° and declination 23.45°, the altitude is 73.45° because 90° − 40° + 23.45° = 73.45°. The shaded height is the window height plus the offset, so 1.5 m + 0.3 m = 1.8 m. That gives a required projection of about 0.54 m.
That example is useful because it separates the geometry into two parts. First, the sun angle tells you how steeply the shadow falls across the facade. Second, the combined shaded height tells you how far down the wall that shadow must travel before the glass is protected. If you change either latitude or declination, the projection follows immediately.
Latitude sensitivity: how passive-solar overhang depth shifts by site
The table below keeps the default window height and offset but changes latitude so you can see how strongly site location affects the result. The pattern is the one you would expect from the tangent relationship: lower-latitude sites need shallower projections, while higher-latitude sites need deeper ones because the noon sun sits lower in the sky.
| Latitude (°) | Solar Altitude (°) | Required Length (m) | Design note |
|---|---|---|---|
| 30 | 83.45 | 0.21 | The noon sun is high, so a shallow overhang can do most of the work. |
| 40 | 73.45 | 0.54 | This is the default passive-solar case shown by the calculator. |
| 50 | 63.45 | 0.90 | The sun is lower, so the shade has to reach farther out from the wall. |
In practical terms, that means a dimension that looks reasonable on one site may be badly undersized on another. The calculator makes the relationship visible so you can compare options instead of relying on intuition alone. If the overhang has to fit within an existing roofline, the sensitivity table is a quick reminder that latitude can determine whether the project needs a small trim detail or a much deeper structural change.
How to interpret the result for passive-solar design
The results panel reports the calculated solar altitude, the vertical span being shaded, and the projection length needed to block direct sun on the selected design day. Read the output as a geometry check, not as a promise of year-round performance. The most important questions are simple: does the unit make sense, does the depth fit the facade, and does the answer move in the expected direction when the inputs change?
If the number seems reasonable, compare it to the actual architectural space available. Fascia depth, roof framing, and the finished look of the facade all affect whether the projection is buildable. If you want to keep a record, the Copy Result button can store the result text so you can paste it into design notes or an email. That is often easier than recreating the input set later from memory.
Limitations and assumptions for fixed overhangs
This calculator is intentionally narrow so the result stays easy to understand. It assumes a straight horizontal overhang, a single design-day declination, and the noon sun angle implied by the latitude you enter. It does not simulate the full year, the entire day, or shadowing from nearby buildings and trees.
- Orientation: the result is most directly useful for the facade you are actually studying; windows that are rotated away from the main direction may need separate morning or afternoon checks.
- Shading geometry: the page sizes one overhang only. It does not blend roof eaves, balconies, fins, awnings, or vegetation into a combined model.
- Site conditions: surrounding walls, overhang-to-glass setbacks, interior blinds, and reflective surfaces can change actual performance even when the geometry looks correct.
- Buildability: the calculator does not account for structural depth, fastening, waterproofing, or aesthetic constraints.
- Design-day choice: the declination you enter is a target for sizing, not a guarantee that every warm day will behave the same way.
Use the result as a first-pass dimension for passive solar planning, then verify it against the real window layout and any local construction constraints before committing to drawings or fabrication.
How passive solar overhang geometry works in solar-noon shading
The geometry is simple enough to sketch by hand, which is why the calculator can stay compact. At solar noon on the design day, the sun’s altitude defines the angle of the shadow line. The overhang creates a right triangle, and the calculator uses that triangle to convert the vertical span you want shaded into a horizontal projection.
Because the page uses latitude and declination, it can be applied to many passive-solar projects without changing the structure of the calculation. A summer design day at one latitude may need only a modest projection, while the same opening at a higher latitude can need a noticeably deeper overhang. That difference is not arbitrary; it comes directly from the tangent relationship between the sun angle and the shadow length.
When you want to think in reverse, the same relation can be rearranged on paper from a known altitude and declination.
The shaded vertical span is the window height plus the offset to the underside of the overhang, so the calculator keeps those values together when it builds the shadow triangle.
That relation is the one to keep in mind if you are adjusting the overhang depth after a concept sketch. Increase the shaded height and the projection grows. Increase the offset and the projection grows. Move to a site with a lower noon sun and the projection grows again. The equation keeps those trade-offs visible instead of hiding them inside a rule of thumb.
That conversion is why the calculator can work from degrees while still using trigonometric functions accurately. It also explains why very small changes in the angle can have a noticeable effect on the projection. As the sun gets lower, tangent changes quickly, and the needed overhang depth rises just as quickly.
That limit is the high-sun end of the problem: as the shadow ray approaches vertical, the horizontal projection needed to shade a given height becomes very small. The opposite end behaves the other way.
In other words, a nearly horizontal sun would demand an impractically long shade. That is one reason passive-solar overhangs are best treated as targeted seasonal devices rather than universal sun blockers. They work well when the design day and facade orientation are chosen carefully, but they are not a substitute for a full shading strategy where low-angle morning or evening sun is a concern.
For practical design work, the main value of the calculator is not just the number itself but the clarity it gives to trade-offs. If you increase the shaded height, the projection must grow. If you move the overhang higher above the window, the projection must also grow. If you move to a site with a lower noon sun, the overhang must reach farther out. Those are all easy decisions to reason through once the geometry is laid out explicitly.
When the overhang is part of a larger architectural composition, you can use the result as a starting point for refinement. A deeper eave might be paired with lighter glazing, an interior thermal mass strategy, or operable blinds. A shallower eave might still work if the window is smaller, the offset is reduced, or the design target uses a slightly different declination. The calculator keeps those options visible by turning a vague shading goal into a measurable dimension.
Further design checks for passive solar overhangs
After you have a first-pass projection, it is worth testing a few additional design questions. One is whether the chosen declination is aggressive enough for your climate. Some designers size for the hottest period of the season; others prefer a slightly earlier target so the window starts getting shade before the peak heat arrives. The calculator can support either approach because declination is an input rather than a fixed assumption.
Another question is how much of the facade the overhang must protect. A tall window, a transom, or a clerestory can change the required length significantly even when the same latitude is used. That is why the shaded height input matters so much: it represents the actual vertical segment of glass that needs to stay out of direct sun. If the protected zone is only part of the opening, you may be able to use a shorter projection than a full-height shade would require.
It also helps to think about the overhang as part of a whole-building shading strategy. A horizontal projection is strongest when the sun is high, but lower-angle sun from the morning or afternoon may still reach the glass. In those situations, vertical fins, side walls, landscaping, or adjacent structures can make a meaningful difference. The calculator does not combine all those effects, but it gives you a clean baseline for the horizontal piece of the problem.
If the project is a retrofit, you may also want to compare the calculated length with the existing roof edge, structural support, and drainage details. A projection that is technically correct but impossible to frame is not useful. Likewise, a projection that works thermally but looks out of proportion may be rejected for aesthetic reasons. The value of the calculator is that it gets the geometry out of the way early, so you can focus on the real constraints once the shading target is known.
Finally, remember that the result is a design guide, not a building verdict. A good passive-solar overhang usually emerges from several iterations: choose a target declination, test the height and offset, check the buildability, and then decide whether a slightly deeper or shallower version still meets the comfort goal. The calculator is built to support that workflow by giving you a quick, repeatable answer each time the inputs change.
Whether you are working on a new house, a renovation, or a conceptual study, the same basic method applies. Measure the window, select the seasonal target, and let the shadow triangle tell you the overhang depth. The rest of the design—materials, framing, drainage, and appearance—can then be evaluated with the right scale already in mind.
Shade Keeper: an overhang mini-game
The noon sun does not hold still across the seasons, and neither will it here. In this game the sun drifts higher and lower while you slide the eave in and out, trying to keep its shadow parked right at the window sill. Deepen the overhang when the sun sinks, pull it back when the sun climbs, and watch the same tangent relationship the calculator uses decide whether the glass stays cool or starts to bake. Click to play, survive sixty seconds, and beat your best score.
Score
Heat
Time
Best
Use ← and → (or drag/tap on the drawing) to change how far the overhang reaches. Keep the shaded edge at or below the sill without wasting eave depth. If sunlight spills onto the glass the heat meter climbs — let it hit 100% and the run ends.