Grazing Angle

The Grazing Angle calculator computes the angle above the horizon to a radar antenna.

INSTRUCTIONS: Choose units and enter the following:

• (R)  This is the range to the radar.
• (h)  This is the height of the radar.

Grazing Angle (ψ):" The calculator return the grazing angle in degrees.  However this can be automatically converted to other angle units via the pull-down menu.  To compute the Grazing Angle considering the curvature of the Earth, CLICK HERE.

The Math / Science

 The formula for the grazing angle is:

   `ψ_g = sin^(-1) (h/R)`

where:

• ψ_g = grazing angle
• R = range to radar
• h = height of radar

The Grazing Angle equation¹ calculates the angle between a target and a radar antenna.  This equation is named for a very particular situation, but at its heart, it's just trig.  Please see the picture.  This equation is based on simple math, but it's helpful in the context of calculating the Signal-to-Noise of a Synthetic Aperture Radar.

Radar Calculators

• SNR Gain Due to Azimuth Processing (coherent pulse integration)
• SNR Gain Due to Range Processing (pulse compression)
• Target Radar Cross Section
• Monostatic SAR Transmitter Antenna Gain Factor
• Radar Atmospheric Loss
• SAR Duty Factor
• Grazing Angle
• Slant Range
• Slant Range (Beta Angle)

3D Vector Calculator Functions

• k V - scalar multiplication
• V / |V| - Computes the Unit Vector
• |V| - Computes the magnitude of a vector
• U + V - Vector addition
• U - V - Vector subtraction
• |U - V| - Distance between vector endpoints.
• |U + V| - Magnitude of vector sum.
• V • U - Computes the dot product of two vectors
• V x U - Computes the cross product of two vectors
• Vector Angle - Computes the angle between two vectors
• Vector Area - Computes the area between two vectors
• Vector Projection - Compute the vector projection of V onto U.
• Vector Rotation - Compute the result vector after rotating around an axis.
• (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
• (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
• (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
• (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates

1. ^ Performance Limits for Synthetic Aperture Radar - Second Edition.  Sandia National Laboratories, Albuquerque, NM.  Printed February 2006.