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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
Critical frequency foF2 (MHz)
Reflecting layer
Effective layer height (km)
Distance to the other station (km)
Minimum takeoff angle (°)
Earth curvature factor k
Result
MUF for a single hop
Operating frequency (85 % of MUF)
Secant multiplier
Number of hops
Length of one hop
Longest hop at this angle
Geometric hop limit (0° elevation)

📐 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 and hop length calculator». 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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