Okumura-Hata Urban Path Loss Calculator

Calculate empirical macrocellular median path loss ($L_{50}$) for VHF/UHF wireless links across dense urban cores, small/medium cities, suburban terrain, and open rural clutter.

dBm
+
dBi
Typical Empirical Presets
Empirically Valid / Strict Hata Bounds
Multi-Clutter Environment Matrix Simultaneous Evaluation
Dense Urban
139.02 dB
Medium City
137.42 dB
Suburban
122.18 dB
Rural Open
100.41 dB
Mobile Correction a(hm)
0.01 dB
h_m = 1.5 m elevation
Clutter Offset vs. Urban
0.00 dB
Reference urban baseline
Attenuation Slope Factor (s)
35.22 dB/dec
Effective exponent n = 3.52
Free Space Loss (FSPL)
105.54 dB
Excess clutter loss: +31.88 dB
Received Power (Prx / RSSI)
−79.42 dBm
11.43 pW (EIRP = 58 dBm)
Wavelength & Path Exponent
33.31 cm
f = 900.0 MHz
Analytical Substitution Chain Okumura-Hata 1980 Formulation

From Empirical Curves to Closed-Form Equations: Okumura to Hata

In 1968, Yoshihisa Okumura and his team at Nippon Telegraph and Telephone (NTT) published an exhaustive experimental campaign measuring wireless signal attenuation across Tokyo, Japan. Using mobile laboratory vehicles equipped with precision receivers, Okumura mapped received field strength across diverse environments ranging from high-rise commercial corridors to residential suburbs and open agricultural terrain.

While Okumura’s findings became the foundation of modern cellular radio planning, the results were cataloged strictly as a series of graphical chart curves. In 1980, Japanese engineer Masaharu Hata performed a rigorous mathematical regression analysis on Okumura’s experimental dataset, publishing closed-form parametric formulas in the seminal IEEE paper "Empirical Formula for Propagation Loss in Land Mobile Radio Services".

Strict Parametric Boundaries of the Hata Model
Hata’s equations represent a statistical polynomial fit to real-world measurements and are strictly valid within the following bounds:
• Carrier Frequency ($f$): $150\text{ MHz} \le f \le 1500\text{ MHz}$
• Base Station Antenna Height ($h_b$): $30\text{ m} \le h_b \le 200\text{ m}$
• Mobile Terminal Antenna Height ($h_m$): $1\text{ m} \le h_m \le 10\text{ m}$
• Link Distance ($d$): $1\text{ km} \le d \le 20\text{ km}$
Operating outside these bounds introduces mathematical divergence, which prompted subsequent extensions such as the COST 231 Hata model for frequencies up to $2000\text{ MHz}$.

Standard Urban Core Formulation & Mobile Correction Factor $a(h_m)$

The foundation of the Hata model is the median path loss in a standard urban environment ($L_{\text{urban}}$), defined as:

Okumura-Hata Urban Core Path Loss Equation
L_{50}(\text{urban, dB}) = 69.55 + 26.16\log_{10}(f) - 13.82\log_{10}(h_b) - a(h_m) + \left[44.9 - 6.55\log_{10}(h_b)\right]\log_{10}(d)
Where $f$ is frequency in MHz, $h_b$ is base station effective height in meters, $d$ is path distance in kilometers, and $a(h_m)$ is the mobile antenna height correction factor in dB.

Because mobile terminals operate within the street-level multipath clutter layer (surrounded by vehicles, curbs, and buildings), the mobile antenna height correction factor $a(h_m)$ depends heavily on urban density:

Mobile Correction Factor: Medium & Small Cities
a(h_m) = \left[1.1\log_{10}(f) - 0.7\right]h_m - \left[1.56\log_{10}(f) - 0.8\right] \quad\text{(dB)}
Valid across all frequencies $150\text{ MHz} \le f \le 1500\text{ MHz}$. For a typical handset height $h_m = 1.5\text{ m}$ at $900\text{ MHz}$, $a(h_m) \approx 0.015\text{ dB}$.
Mobile Correction Factor: Large Dense Cities
a(h_m) = \begin{cases} 8.29\left[\log_{10}(1.54 h_m)\right]^2 - 1.1 & \text{for } f \le 200\text{ MHz} \text{ (or } < 300\text{ MHz)} \\ 3.2\left[\log_{10}(11.75 h_m)\right]^2 - 4.97 & \text{for } f \ge 400\text{ MHz} \text{ (or } \ge 300\text{ MHz)} \end{cases}
Reflects the severe optical shadowing and lack of grazing multipath rays in dense metropolitan canyons lined with high-rise structures.

Clutter Corrections: Suburban and Open Rural Regressions

Signal propagation through residential suburbs and open countryside experiences substantially lower attenuation due to the absence of towering concrete street canyons. Hata introduced empirical correction offsets subtracted directly from the standard urban baseline:

Suburban Area Path Loss Equation
L_{\text{suburban}}(\text{dB}) = L_{\text{urban}} - 2\left[\log_{10}\left(\frac{f}{28}\right)\right]^2 - 5.4
Accounts for low-density residential housing, trees, gardens, and wide roads. At $900\text{ MHz}$, suburban clutter provides a $\approx 15.2\text{ dB}$ reduction in path loss compared to urban environments.
Open / Rural Area Path Loss Equation
L_{\text{open}}(\text{dB}) = L_{\text{urban}} - 4.78\left[\log_{10}(f)\right]^2 + 18.33\log_{10}(f) - 40.94
Models open farmland and rural prairies devoid of tall trees or structures. At $900\text{ MHz}$, open clutter eliminates $\approx 37.0\text{ dB}$ of path loss compared to urban cores.

Engineering Significance of the Distance Exponent ($s$)

In free space, received power rolls off at $20\text{ dB/decade}$ ($1/d^2$ law). In the Okumura-Hata model, the distance dependency is governed by the slope term:

Distance Attenuation Slope & Path Loss Exponent
s = 44.9 - 6.55\log_{10}(h_b) \quad\text{(dB/decade)} \quad\implies\quad n = \frac{s}{10}
Where $n$ is the classical empirical path loss exponent ($P_{\text{rx}} \propto 1/d^n$).

This equation reveals a profound cellular planning principle:

  • At minimum tower height $h_b = 30\text{ m}$, the slope is $s = 44.9 - 6.55\log_{10}(30) = 35.22\text{ dB/decade}$ ($n \approx 3.52$).
  • At maximum tower height $h_b = 200\text{ m}$, the slope flattens to $s = 44.9 - 6.55\log_{10}(200) = 29.83\text{ dB/decade}$ ($n \approx 2.98$).

Elevating the macro base station mast not only increases direct Line-of-Sight clearing over average rooftop clutter heights, but physically flattens the attenuation slope per decade of distance, dramatically expanding the effective cell radius.

Standard Reference Benchmark Table (hb = 30 m, hm = 1.5 m)

Benchmark Okumura-Hata median path loss ($L_{50}$) across standard land mobile radio, public safety, and cellular spectrum bands:

Band & Frequency Distance (d) FSPL Baseline Dense Urban (L50) Medium City (L50) Suburban (L50) Open Rural (L50)
150 MHz (VHF Land Mobile) 2 km 82.0 dB 114.2 dB 114.2 dB 103.5 dB 88.4 dB
150 MHz (VHF Land Mobile) 10 km 96.0 dB 138.8 dB 138.8 dB 128.1 dB 113.0 dB
450 MHz (PMR / UHF Public) 3 km 95.1 dB 132.8 dB 131.2 dB 120.4 dB 102.7 dB
450 MHz (PMR / UHF Public) 10 km 105.5 dB 151.3 dB 149.7 dB 138.9 dB 121.2 dB
700 MHz (LTE Band 28) 2 km 95.4 dB 134.1 dB 132.4 dB 118.8 dB 98.6 dB
700 MHz (LTE Band 28) 5 km 103.3 dB 148.1 dB 146.4 dB 132.8 dB 112.6 dB
850 MHz (Cellular 850) 1 km 91.0 dB 123.1 dB 121.5 dB 106.6 dB 85.3 dB
850 MHz (Cellular 850) 5 km 105.0 dB 151.0 dB 149.4 dB 134.5 dB 113.2 dB
850 MHz (Cellular 850) 15 km 114.6 dB 167.8 dB 166.2 dB 151.3 dB 130.0 dB
900 MHz (GSM 900) 2 km 97.6 dB 139.0 dB 137.4 dB 122.2 dB 100.4 dB
900 MHz (GSM 900) 10 km 111.5 dB 163.6 dB 162.0 dB 146.8 dB 125.0 dB
1500 MHz (Model Bound) 5 km 109.9 dB 159.2 dB 157.6 dB 139.7 dB 115.6 dB

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