Urban path loss calculator: Hata and COST-231
A model that leaves its range of validity in silence
Hata describes average loss in built-up areas, and it does it well — within its limits. The trouble is that outside them it says nothing and simply produces a number. That bites radio amateurs particularly: a typical antenna on a house roof stands ten metres up, while the model starts at thirty.
| Model | |
| Frequency (MHz) | |
| Base station antenna height (m) | |
| Mobile antenna height (m) | |
| Distance (km) | |
| Terrain type | |
| Result | |
| Path loss | |
| Mobile height correction a(hm) | |
| Free-space loss for comparison | |
| How much the city adds | |
| Within the model's range of validity | |
📐 The formulas
Correction for the mobile's height:
small and medium city: a(hm) = (1.1·log f − 0.7)·hm − (1.56·log f − 0.8)
large city, f ≥ 400: a(hm) = 3.2·(log(11.75·hm))² − 4.97
Okumura–Hata, urban:
L = 69.55 + 26.16·log f − 13.82·log hb − a(hm) + (44.9 − 6.55·log hb)·log d
Suburban: L_urban − 2·[log(f/28)]² − 5.4
Open terrain: L_urban − 4.78·(log f)² + 18.33·log f − 40.94
COST-231 Hata (1500…2000 MHz):
L = 46.3 + 33.9·log f − 13.82·log hb − a(hm) + (44.9 − 6.55·log hb)·log d + Cm
Cm = 0 (suburban / medium city) or 3 (metropolitan)
Range of validity:
| Parameter | Hata | COST-231 |
|---|---|---|
| Frequency | 150…1500 MHz | 1500…2000 MHz |
| Distance | 1…20 km | 1…20 km |
| Base station height | 30…200 m | from 30 m |
| Mobile height | 1…10 m | 1…10 m |
Where this calculator stops:
- The model is empirical: it describes an average over a large area, not a particular street
- Outside its range of validity the calculator still shows a number, but says plainly that it should not be trusted
- For an antenna on a house roof (hb ≈ 10 m) Hata does not apply — which is exactly where people most want to use it
- The spread about the average is units to tens of decibels, depending on the particular buildings
🎯 In practice
- Estimating repeater coverage in a town.
- Comparing with free space: you can see exactly what the buildings add.
- Understanding why “the calculation said it should be enough” — the difference often exceeds 40 dB.
Practical advice:
- Look first at the difference from FSPL: it shows what the town costs you.
- At amateur antenna heights the model overstates the loss — treat it as a pessimistic estimate.
- In open terrain Hata approaches the two-ray model, and there you are better off using that.
- Real measurements always beat any model: drive round with a receiver.
© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.
How to cite this calculator
UR3PKI. «Urban path loss calculator: Hata and COST-231». CyberDev.Space. https://cyberdev.space/en/radio/calculators/others/hata (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.