Angle of Incidence Calculator — Law of Reflection
Enter the vertical height of the source above a flat surface and the horizontal offset to find the angle of incidence — measured from the surface normal — along with the equal angle of reflection and the complementary grazing angle.
m
m
Angle between the incoming ray and the surface normal at the point of contact
- 1
Path length (hypotenuse)
√(4² + 3²) = 5 - 2
Angle (radians)
arctan(3 ÷ 4) = 0.643501 - 3
Angle of incidence
0.643501 × (180 ÷ π) = 36.87
How does this calculator work?
Angle of incidence θᵢ = arctan(d / h), where h is the source height above the surface and d is the horizontal offset. By the law of reflection the reflected ray leaves at the same angle. The grazing angle = 90° − θᵢ. For h = 4 m and d = 3 m, θᵢ = arctan(3/4) ≈ 36.87°.
Formula
How this is calculated
The angle of incidence (θᵢ) is defined as the angle between the incoming ray and the normal to the surface at the point of contact. The normal is the line perpendicular to the surface — for a horizontal surface, it points straight up. If the source is at vertical height h above the surface and displaced horizontally by d, the ray travels along the hypotenuse of the right triangle formed by h and d. The angle this ray makes with the vertical normal is θᵢ = arctan(d / h).
At d = 0 the ray strikes straight down (normal incidence, θᵢ = 0°) and bounces straight back. As d increases relative to h, θᵢ approaches 90° (grazing incidence). The grazing angle is the complement: 90° − θᵢ — the angle measured from the surface itself rather than the normal. X-ray reflectometry and radar use the grazing-angle convention.
The law of reflection states that the reflected ray leaves at the same angle as the incident ray (θᵣ = θᵢ), on the opposite side of the normal, in the same plane. This is an exact geometric result for specular (mirror-like) reflection from a flat surface and holds for all wave types — light, sound, and radio waves — as long as the surface is smooth compared with the wavelength.
Frequently asked questions
The angle of incidence is measured from the surface normal (perpendicular to the surface); the grazing angle is measured from the surface itself. They are complementary: θ_grazing = 90° − θ_incidence. Grazing angles near zero mean almost tangential reflection; these are the conditions used in X-ray mirrors and fibre-optic cladding.
Yes — the law of reflection (angle in = angle out, both from the normal) holds for any wave at a smooth flat boundary: visible light, sound, radio, and water waves. It breaks down when surface roughness is comparable to the wavelength, causing diffuse scattering instead of a single reflected beam.
Subtract the grazing angle from 90°: θ_incidence = 90° − θ_grazing. For instance, a ray that makes a 20° angle with the surface has an angle of incidence of 70° from the normal. Equivalently, arctan(d/h) = 90° − arctan(h/d).
Also known as
TG we-Calculate Editorial Team. (2026). Angle of Incidence Calculator — Law of Reflection [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/angle-of-incidence-calculator
TG we-Calculate Editorial Team. "Angle of Incidence Calculator — Law of Reflection." TG we-Calculate. 2026. https://we-calculate.com/calculator/angle-of-incidence-calculator.
TG we-Calculate Editorial Team, "Angle of Incidence Calculator — Law of Reflection," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/angle-of-incidence-calculator
@misc{wecalculate_angle_of_incidence_calculator, title = {Angle of Incidence Calculator — Law of Reflection}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/angle-of-incidence-calculator}}, year = {2026}, note = {TG we-Calculate} }
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