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MUF and hop length calculator

One number that cannot be calculated

The MUF is easy to work out — from the critical frequency foF2 and the geometry of the hop. But foF2 itself cannot be calculated: it is measured by ionosondes and it changes every hour. So this calculator answers the question “what happens if foF2 is such and such”, not “what is it right now”.

F2 layer, h ≈ 300 kmD 2000 km
The lower the angle, the longer the hop and the higher the MUF
Result

📐 The formulas​

The secant law:

MUF = k · foF2 · √( 1 + (D / (2·h))² )

where D is the length of one hop, h the effective layer height, and k = 1.0…1.2 a correction for the curvature of the Earth.

The longest single hop for a minimum takeoff angle ε:

sin ψ = R·cos(ε) / (R + h)
θ = 90° − ε − ψ
D_max = 2 · R · θ

Range of a single hop:​

Layer0° (geometric limit)3° (in practice)
E (110 km)2351 km1776 km
F2 (300 km)3836 km3224 km

A check point:​

foF2 = 8 MHz, h = 300 km, D = 2000 km → secant factor 3.48, MUF = 27.8 MHz. At D = 0 (vertical sounding) the MUF equals foF2 itself — that is the main sanity check.

Where this calculator stops:
  • foF2 is a measured quantity. Take it from an ionospheric map for the moment in question, or the calculation means nothing
  • A flat-Earth model with the correction k: on very long paths it is inaccurate, which is why the MUF is worked out for a single hop
  • The effective layer height also varies: 300 km for F2 is an average, in reality 250…400
  • The LUF (the lower limit set by absorption in the D layer) is not calculated here: that needs solar activity data

🎯 In practice​

  • Choosing a band: if the MUF is 27 MHz then 20 metres works and 10 is marginal.
  • Estimating the number of hops to the other station.
  • Understanding why a low-angle antenna is better for DX — a longer hop and a higher MUF.
Practical advice:
  1. Work at 80–90 % of the MUF: the signal is steadier there and the absorption lower.
  2. The greater the distance, the higher the MUF — which is why distant stations are audible on bands where nearby ones are silent.
  3. Each hop costs several decibels at the ground reflection: five hops is already noticeable.
  4. Look for current foF2 on ionospheric maps; they usually carry a ready-made MUF map as well.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «MUF Calculator: Maximum Usable Frequency and Hops». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/muf/ (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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