Shadow length from sun angle calculator

Enter the height in any length unit and the solar elevation in degrees above the horizon. The result uses the same unit as the height. It is a quick, deterministic way to plan shade, explore solar geometry, prepare a photograph, or check a right-triangle calculation without drawing the triangle by hand.

Enter a vertical height and a valid solar elevation

Start with the vertical height of the object that casts the shadow. You may use metres, feet, centimetres, inches, or another length unit because the calculator preserves that unit in the resulting shadow length. Measure from the point where the object meets the ground to its top, and make sure the object is upright. Then enter the Sun's elevation angle in degrees above the local horizon. The angle must be greater than zero and less than ninety degrees. An angle near zero describes sunlight close to the horizon and produces a very long theoretical shadow. An angle near ninety describes sunlight almost overhead and produces a very short one. Do not enter a zenith angle, compass bearing, or azimuth: those are different measurements. If a source gives the zenith angle instead, subtract it from ninety degrees before using this calculator. For meaningful field estimates, the ground should be approximately level and the shadow should fall without interruption from walls, trees, or changes in terrain.

Understand the cotangent relationship

A vertical object, its horizontal shadow, and a straight ray of sunlight form a right triangle in the simplified model. The object height is opposite the Sun's elevation angle, while the shadow is adjacent to that angle. Tangent therefore equals height divided by shadow length. Rearranging the equation gives shadow length equals height divided by the tangent of the elevation angle, which is also height multiplied by the cotangent of that angle. The calculator converts degrees to radians for the trigonometric operation and rounds the reported numeric values to twelve decimal places for stable machine-readable output. At forty-five degrees, tangent is one, so the shadow and object have equal lengths. Below forty-five degrees the shadow is longer than the object; above forty-five degrees it is shorter. The returned shadow-to-height ratio makes that relationship explicit and can be reused for several objects under the same sunlight. Doubling the height doubles the predicted shadow, while changing the angle affects every object through the same cotangent ratio.

Interpret the estimate and its practical limits

Treat the result as an ideal geometric estimate, not a surveyed boundary or a complete solar-position forecast. The model assumes a perfectly vertical object, level ground, straight incoming light, and a clearly defined ray from the top of the object. Real shadows may differ because the ground slopes, the object leans, the Sun has a visible disk rather than being a point, and atmospheric refraction matters near the horizon. A fuzzy shadow edge also makes physical measurement less exact than the decimal output suggests. The calculator does not determine the elevation angle from a date, time, latitude, or longitude; obtain that angle from an appropriate solar-position source and then use it here. For garden or photography planning, compare several plausible angles to see how shade changes during the day or season. For construction setbacks, solar access rules, surveying, navigation, or safety-critical work, use the standards, professional instruments, and tolerances required for that field. Never look directly at the Sun to estimate its angle; use published solar data or safe indirect measurement methods.