Calculate maximum usable frequency, critical frequency, or incidence angle from any two values with frequency units from Hz to GHz.

Ideal secant-law estimate for ionospheric propagation. It does not predict current conditions or guarantee a working radio link.

0° is vertical incidence; angle must be below 90°.

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Maximum Usable Frequency Formula

The following formula is used to calculate the maximum usable frequency (MUF) for a given critical frequency and incidence angle.

MUF = fc / cos(θ)

Variables:

  • MUF is the maximum usable frequency
  • f_c is the critical frequency
  • (theta) is the angle from the normal at the ionospheric layer: 0° for vertical incidence and less than 90°. The calculator also accepts radians; this is not the antenna elevation angle.

To calculate the maximum usable frequency, divide the critical frequency by the cosine of the incidence angle.

What is Maximum Usable Frequency?

The maximum usable frequency (MUF) is the highest frequency at which a radio wave can be transmitted between two points via reflection from the ionosphere. It is an important parameter in the field of radio communications, particularly for long-distance communication. The MUF depends on the critical frequency of the ionosphere and the angle at which the radio wave is transmitted. The secant-law calculator is an ideal estimate. Actual usable frequencies vary with path, time and ionospheric conditions; the estimate does not ensure reliable signal transmission.

How to Calculate Maximum Usable Frequency?

The following steps outline how to calculate the Maximum Usable Frequency (MUF).

  1. First, determine the critical frequency (f_c).
  2. Next, determine the incidence angle from the normal at the layer, in degrees or radians, from 0° up to but excluding 90°.
  3. Next, calculate the cosine of the incidence angle.
  4. Finally, calculate the Maximum Usable Frequency (MUF) using the formula MUF = f_c / (cos(theta)).
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Critical Frequency (f_c) = 5 MHz

Incidence Angle ((theta)) = 45 degrees from the layer normal. The estimate is MUF = 5/cos(45°) ≈ 7.0711 MHz.