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Doppler Radar Speed & Frequency Shift Calculator

Calculate radar Doppler frequency shift (fd), target velocity in MPH and m/s, and cosine angle error across X-band, K-band, and Ka-band police radar frequencies.

0° = directly head-on; 15° = standard roadside patrol car parked on shoulder

Calculation Results

Doppler Frequency Shift (fd): 7,508 Hz 103.55 Hz shift per 1 MPH on Ka-Band
Radar Indicated Speed (Cosine Effect): 72.4 MPH Reads 2.6 MPH lower in driver's favor
True Velocity in Metric: 120.7 km/h (33.52 m/s)
Radar Radar Wave Wavelength (λ): 8.64 mm

About This Calculator

Calculate radar Doppler frequency shift (fd), target velocity in MPH and m/s, and cosine angle error across X-band, K-band, and Ka-band police radar frequencies.

Frequently Asked Questions

What is the Doppler radar equation for moving vehicles?

The Doppler frequency shift is given by fd = (2 * v * f0 * cos θ) / c, where v is target velocity, f0 is carrier frequency, θ is the angle between the radar beam and the vehicle's direction of travel, and c is the speed of light.

What is the 'Cosine Effect' in police radar enforcement?

When a police officer aims radar from the shoulder of a highway, the angle reduces the measured component of velocity (V_measured = V_true * cos θ). Because the cosine of any positive angle is less than 1.0, the radar always displays a speed lower than the vehicle's actual speed, benefiting the driver.

What are the standard police radar frequencies in the US?

In the United States, police radar operates on three FCC-allocated bands: X-Band (10.525 GHz), K-Band (24.150 GHz), and Ka-Band (typically 33.8 GHz to 35.5 GHz). Ka-band is the modern standard offering narrow beamwidths and minimal detection range for radar detectors.

Why does the Doppler formula multiply by 2?

The factor of 2 occurs because the Doppler shift happens twice: once when the incoming electromagnetic wave hits the moving vehicle, and a second time when the reflected wave bounces back to the stationary radar antenna.