Solar guide · Shadow calculation table
Estimating Shadow Direction from Solar Angles
Calculate a Perth shadow bearing and length step by step from solar azimuth, altitude, and a two-metre object height.
- Published
- Updated
A sun-facing object casts its shadow away from the Sun. On a compass plan, the first estimate is therefore simple: add 180° to solar azimuth and wrap the result back into the 0–360° range. If the Sun is at 70°, the level-plan shadow bearing is approximately 250°.
Length needs another assumption. For a vertical object on level ground, the shadow-length-to-height ratio is 1 ÷ tan(solar altitude). This idealized relationship is useful for scale intuition, but a real result changes with sloped ground, tilted objects, irregular shapes, diffuse light, and intervening obstructions.
Reverse the bearing, then check altitude
To reverse a solar bearing, add 180°. If the result is 360° or more, subtract 360°. The direction is meaningful for direct sunlight only when the Sun is above the horizon and reaches the object without being blocked.
Altitude controls the theoretical length. At 45°, the level-ground shadow of a vertical object is approximately the same length as the object’s height. Below 45° the ratio grows; above 45° it shrinks. As altitude approaches zero, the ideal ratio becomes extremely large and increasingly sensitive to terrain and skyline assumptions.
Keep the geometric model explicit
A shadow estimate needs an object height, a receiver plane, and a solar position for a particular instant. Without those definitions, a direction arrow can be useful but a claimed length is not reproducible.
This guide reports a dimensionless ratio. Multiply it by the object height only when the object is vertical and the receiving ground is approximately level. More complex cases require three-dimensional geometry or site measurement.
These are fixed seasonal reference dates, not the exact local dates of the solstices or equinoxes.
Shadow calculation table
Perth two-metre shadow direction test
A two-metre vertical object in Perth is evaluated every two hours from 08:00 to 16:00 on 20 March 2026. Shadow bearing is (solar azimuth + 180) mod 360; theoretical length is object height divided by tan(solar altitude). No length is emitted when altitude is at or below 0°.
Direction
shadow bearing = (azimuth + 180) mod 360
Length on level ground
length = 2 m / tan(altitude)
Calculated example — not a field measurement
A task you can reproduce
Calculate the direction and level-ground length of a two-metre post’s shadow at 10:00 in Perth, then compare it with morning, noon, and afternoon results.
- Observation point
- Perth, Western Australia, Australia
- Coordinates
- -31.9523°, 115.8613°
- Timezone and model
- Australia/Perth · SPT-SUN-V1
- Reference dates
- 2026-03-20
Work the 10:00 result step by step
1. Reverse the solar bearing
(54.5° + 180°) mod 360° = 234.5°
The shadow points 234.5° South-west, directly away from the calculated Sun bearing.
2. Calculate the level-ground length
2.0 m ÷ tan(43.5°) = 2.11 m
The displayed result uses the full engine value before rounding the labels shown here.
Compare lower and higher Sun angles
08:00
Altitude 20.3°
Shadow 5.41 m
12:00
Altitude 57.9°
Shadow 1.26 m
16:00
Altitude 30.2°
Shadow 3.44 m
Lower positive altitude produces a longer level-ground shadow. At the same altitude, doubling the object height from 2.0 m to 4.0 m doubles this theoretical shadow from 2.11 m to 4.21 m.
Reproduce the case
- 1. Open the Sun Position & Angle Calculator.
- 2. Enter the coordinates and date shown in the case inputs, then set the local time to 10:00.
- 3. Copy the displayed azimuth and altitude into the two formulas shown in the worked calculation.
- 4. Reverse the azimuth for the shadow bearing and divide object height by the tangent of altitude for length.
- 5. Stop if altitude is at or below zero, or if the real site does not satisfy the stated assumptions.
Assumptions and stop conditions
- The object is vertical, two metres high, and meets approximately level ground at a right angle.
- Direct sunlight reaches the object without terrain, buildings, trees, or other obstructions.
- The calculation describes hard geometric direction and length; diffuse light, penumbra, and surface slope are outside the model.
- When solar altitude is 0° or lower, this model returns no shadow bearing or length.
| Local time | Solar direction | Altitude | Shadow direction | Shadow length | State |
|---|---|---|---|---|---|
| 2026-03-20 08:00 | 77.2° East | 20.3° | 257.2° West | 5.41 m | Calculated on level ground |
| 2026-03-20 10:00 | 54.5° North-east | 43.5° | 234.5° South-west | 2.11 m | Calculated on level ground |
| 2026-03-20 12:00 | 11.6° North | 57.9° | 191.6° South | 1.26 m | Calculated on level ground |
| 2026-03-20 14:00 | 319.8° North-west | 51.2° | 139.8° South-east | 1.61 m | Calculated on level ground |
| 2026-03-20 16:00 | 290.9° West | 30.2° | 110.9° East | 3.44 m | Calculated on level ground |
This result assumes a vertical object and level ground. Slope, object shape, diffuse light, terrain, and obstructions can change the visible shadow. It is a geometry estimate, not a surveyed shadow diagram.
Download the evidence dataset
Perth near-equinox bearings and theoretical shadow lengths for a two-metre vertical object from 08:00 to 16:00. The UTF-8 CSV uses a fixed column order and contains calculated values only.
Apply the ratio carefully
For an ideal 2 m vertical post, a displayed ratio of 1.5 implies a 3 m shadow on level ground. Mark that bearing and distance on a plan, then check whether a wall, slope, canopy, or different receiving surface changes the geometry.
For buildings or compliance work, use surveyed dimensions and an appropriate three-dimensional or professional shading analysis. This simplified construction is best used for first-pass reasoning and field-observation planning.
- Shadow bearing = normalized solar azimuth + 180°.
- Level-ground shadow length = object height ÷ tan(solar altitude).
- Do not calculate a direct-sun length when altitude is at or below 0°.
Responsible use
Practical uses and model limits
Terrain and buildings may be displayed in the 3D view for visual context where available. They are not inputs to the solar engine, which reports an unobstructed astronomical baseline without terrain, building, or tree shading.
Useful for
- • Estimating which side of an object will be shaded at a selected time.
- • Choosing field-measurement times when shadows are long enough to observe clearly.
- • Checking whether a simple plan sketch is directionally consistent with the solar bearing.
Do not overlook
- • The ratio assumes a vertical object, level receiver, direct sunlight, and no obstruction between Sun and object.
- • Slopes, facade projections, complex roofs, penumbra, diffuse sky light, and reflected light require a more complete model.
- • This is not a substitute for surveyed shadow diagrams, development-approval evidence, or safety-critical engineering.
Sources and reproducibility
Evidence and calculation sources
- NOAA Solar Calculation Details
Independent background on solar azimuth and elevation conventions; NOAA does not endorse this site.
- SunCalc
Solar position and astronomical event calculations used by this site.
- Luxon
IANA timezone-aware conversion between the selected local time and UTC.
- Solar Path Tracker methodology
Definitions, angle normalization, polar handling, precision, and model limits.