Shadow Length Calculator
Ground shadow length and ratio from height and sun angle.
What it does
Shadows are sun angles drawn on the ground. Low morning sun throws long lines, noon sun pools near feet, and the ratio follows one tangent.
The tool above divides height by tan(angle). A 6 ft pole at 45 degrees throws 6 ft at 1 x height in medium light. The metric match is 1.8 m toward 1.8 m.
Angles set the mood. Under 20 degrees shadows run triple height in photo hour gold, under 50 they read medium, and above they shrink to short midday stubs.
Ratios travel across objects. A 1 x ratio means fences shadow their own height, 3 x means morning yards lie mostly shaded, and 0.4 x means noon patios bake.
Flat math starts the plan. Slopes stretch downhill shadows, daylight saving shifts clock times, and trees add their own shade on top.
How to use
- Pick imperial (ft) or metric (m).
- Enter object height.
- Enter sun angle: 45 suits midday shoulder seasons.
- Read shadow first.
- Read ratio next.
- Read light tag and plan photos or fences.
Formula
- height
- Object standing height.
- angle
- Sun height above horizon, in degrees.
Angle is sun height above the horizon in degrees. Low angles give long ratios, high angles short ones.
Worked example
Example: 6 ft pole, 45 degrees
Imperial defaults: 6 ft pole at 45 degrees. These are also the default values, so the page opens on this answer.
- Pole: 6 ft.
- Sun: 45 degrees.
- Tangent: tan(45) = 1.
- Shadow: 6 / 1 = 6 ft.
- Ratio: 1 / 1 = 1 x height.
- Light: Medium shadows. Tool shows 6 ft, 1 x height, Medium shadows.
Reference table
| Sun | Shadow | Ratio |
|---|---|---|
| 15 deg | 22.4 ft | 3.73 x height |
| 30 deg | 10.4 ft | 1.73 x height |
| 45 deg | 6 ft | 1 x height |
| 60 deg | 3.5 ft | 0.58 x height |
Limits
- Flat ground math only. Slopes shift shadows.
- Angle guesses swing results wide.
- Trees and buildings add shade.
- Time of day needs solar tables.
Common mistakes
- Guessing the angle within 10 degrees.
- Planning fences on noon shadows alone.
- Forgetting daylight saving on clock times.
- Measuring height with shoes and hats.
- Ignoring slope direction.
Try it yourself
Quick checks. Answers sit tucked under each question.
10 ft at 30 degrees?
tan(30) = 0.577. Shadow is 10 / 0.577 = 17.3 ft. Ratio is 1 / 0.577 = 1.73 x height.
2 m at 60 degrees metric?
tan(60) = 1.732. Shadow is 2 / 1.732 = 1.2 m after rounding (1.15). Ratio is 1 / 1.732 = 0.58 x height.
Questions
Shadow of 6 ft at 45 degrees?
Divide height by tangent of the angle. Here 6 / tan(45) = 6 ft.
Low versus high sun?
Low sun near 10 degrees triples height: 6 ft throws 34 ft. High sun near 70 degrees shrinks to 2.2 ft.
What do the light tags mean?
Under 20 reads photo hour, under 50 medium, above short midday. Here 45 is medium.
How do I find the angle?
Measure the angle with a clinometer app or read solar noon tables. Guesses swing shadows wide.
Does slope matter?
Yes. Slope and daylight saving shift real shadows past flat math.
Fence height included?
No. Fence lines and setbacks need local rules.