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Calcimator

HF Propagation Calculator

Estimate Maximum Usable Frequency (MUF), optimum frequency, and hop count from solar flux index, time, distance, and season.

About this calculator

HF signals travel long distances by refracting off the ionosphere's F2 layer, and the Maximum Usable Frequency (MUF) is the highest frequency that will actually bend back to Earth rather than punching through into space for a given path — go above it and your signal just disappears upward. This calculator builds an educational estimate of that critical frequency (foF2) from the Solar Flux Index you enter (higher solar activity ionizes the F2 layer more strongly), a time-of-day factor that peaks at 14:00 UTC in this model (ionization tracks the sun, with F2-layer ionization lagging into the afternoon rather than cresting right at local solar noon), and a seasonal multiplier (F2 ionization tends to run stronger in spring/fall and weaker in summer). It then applies the standard secant law, MUF = foF2 × sec(θ), where θ is the signal's angle of incidence on the ionosphere — computed geometrically from your target distance assuming a 300 km-high F2 layer — since a signal hitting the ionosphere at a shallow, oblique angle over a long path refracts back down at a higher frequency than one hitting it straight overhead.

From MUF it derives the Frequency of Optimum Traffic (FOT, conventionally 85% of MUF, a safety margin against day-to-day MUF variability) and a rough Lowest Usable Frequency (LUF, roughly MUF/3, below which D-layer absorption eats the signal), then recommends an amateur band whose frequency sits near the FOT. Hop count assumes a maximum single-hop distance geometrically limited by that same 300 km ionosphere height, with roughly 8 dB of signal loss estimated per hop. Treat every number here as a simplified daytime-model estimate for learning propagation concepts — real MUF prediction depends on full ionospheric sounding data, your specific ground track's geomagnetic latitude, and whether you're propagating via F2, E, or Es layers, none of which this simplified model captures.

Inputs

km

Results

Max Usable Frequency (MUF)

14.17 MHz

Optimum Frequency (FOT)

12.05 MHz

Lowest Usable Freq (LUF)4.72 MHz
Critical Frequency (foF2)14.13 MHz
Hops Needed2
Total Hop Loss16 dB
Max Single Hop3,956 km
Sec(θ) Factor1
Recommended Band20m (14 MHz) or 17m (18 MHz)
How to Use This Calculator
  1. Enter the current Solar Flux Index (SFI) from WWV, DX bulletins, or propagation websites.
  2. Set the UTC time, path distance to your target (km), and current season.
  3. Review the Maximum Usable Frequency (MUF), Optimum Working Frequency (FOT), and LUF.
  4. Select frequencies at or below the FOT for reliable propagation on this path.
  5. Account for foF2 critical frequency and estimated number of ionospheric hops needed.

How the result changes with Time (UTC)

Time (UTC)Max Usable Frequency (MUF)Optimum Frequency (FOT)
67.42 MHz6.31 MHz
911.17 MHz9.5 MHz
1812.36 MHz10.51 MHz
236.39 MHz5.44 MHz

What each input means

Solar Flux Index (SFI)
10.7cm solar flux index (65-80 = low, 100-150 = moderate, 200+ = high solar activity)
Time (UTC)
Time of day in UTC (local noon ≈ peak ionization)
Target Distance
Distance to target station in kilometers
Season
Current season, which affects ionospheric propagation conditions.

How this is calculated

Formula

MUF = foF2 × sec(θ); FOT = 0.85 × MUF

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Solar Flux Index (SFI) = 120, Time (UTC) = 12, Target Distance = 5000, Season = 1 = 4 input(s) provided
  2. Calculate Max Usable Frequency
    Max Usable Frequency = m
    14.17 = 14.17
  3. Calculate Optimum Frequency
    Optimum Frequency = m
    12.05 = 12.05
  4. Calculate Lowest Usable Freq
    Lowest Usable Freq = m
    4.72 = 4.72
  5. Calculate Critical Frequency
    Critical Frequency
    14.13 = 14.13

Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

What is MUF and why does going above it make my signal disappear?

The Maximum Usable Frequency is the highest frequency that will still refract back to Earth off the ionosphere's F2 layer for a given path; above it, the signal punches through into space instead of bending back down. The calculator derives MUF from an estimated critical frequency (foF2) multiplied by sec(θ), where θ is the signal's angle of incidence on the ionosphere computed from your target distance.

Why does the calculator ask for Solar Flux Index, time of day, and season separately?

Each factors into how strongly the F2 layer is ionized, which sets foF2: higher Solar Flux Index means more solar radiation ionizing the layer, the time-of-day factor peaks around 14:00 UTC in this model since F2-layer ionization lags into the afternoon rather than cresting right at local solar noon, and the seasonal multiplier reflects that F2 ionization tends to run stronger in spring/fall than summer. All three multiply together into the foF2 estimate before the secant-law MUF calculation.

What's the difference between FOT and LUF, and why is the recommended band near FOT rather than MUF?

FOT (Frequency of Optimum Traffic) is set at 85% of MUF as a safety margin against day-to-day MUF variability, while LUF (Lowest Usable Frequency) is roughly MUF/3, below which D-layer absorption eats the signal. The calculator recommends a band near FOT rather than right at MUF because operating too close to MUF risks the path closing as ionization naturally fluctuates.

How is the hop count and per-hop signal loss estimated?

Hop count divides your target distance by the maximum single-hop distance geometrically possible off a 300 km-high F2 layer, rounding up to a whole number of hops. Each hop is assumed to cost a flat 8 dB of signal loss, so total hop loss is simply hopsNeeded × 8 dB — a simplified estimate, not a measurement of actual path loss under real ionospheric absorption conditions.

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