Two-Ray Ground Reflection Loss Calculator
Estimate far-field path loss over flat ground using the two-ray ground-reflection model, which combines the direct signal with the wave reflected off the earth. Because the two rays interfere, signal power falls off with the fourth power of distance (40 dB per decade) rather than the square, so this model predicts more loss with distance than free space for long over-ground links.
Enter Values
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How to use this calculator
- Enter the distance d between the antennas in metres.
- Enter the transmit and receive antenna heights ht and hr in metres above the reflecting ground.
- Optionally enter the transmit and receive antenna gains Gt and Gr in dBi (leave blank for 0 dBi isotropic); read off the two-ray path loss in dB.
How it works
In the far field the two-ray path loss simplifies to PL(dB) = 40·log₁₀(d) − 20·log₁₀(ht) − 20·log₁₀(hr) − Gt − Gr. The 40·log₁₀(d) term is the 1/d⁴ distance dependence; raising either antenna height lowers the loss by 20·log₁₀(h), and antenna gain in dBi is subtracted directly. Note this simplified form drops the wavelength — it is only accurate beyond the crossover distance where the ground-reflected ray has settled into the fourth-power regime.
Worked example
Worked example. For d = 1000 m, ht = 30 m and hr = 10 m with isotropic antennas: 40·log₁₀(1000) = 120 dB, 20·log₁₀(30) = 29.542 dB and 20·log₁₀(10) = 20 dB, so PL = 120 − 29.542 − 20 = 70.458 dB.
Common mistakes
- Using this far-field formula inside the crossover distance — closer than d꜀ ≈ 4π·ht·hr/λ you should use free-space loss, which is lower.
- Adding antenna gains instead of subtracting them: gain reduces path loss, so Gt and Gr are subtracted in the dB equation.
- Mixing units — d, ht and hr must all be in metres and the gains in dBi for the constants to hold.
Frequently asked questions
Why does loss increase at 40 dB per decade instead of 20?
The ground-reflected ray arrives roughly out of phase with the direct ray in the far field, and the partial cancellation makes received power fall as 1/d⁴ (40 dB/decade) rather than the 1/d² (20 dB/decade) of free space.
When should I use free-space loss instead?
Below the crossover distance d꜀ ≈ 4π·ht·hr/λ the two rays have not yet settled into the fourth-power regime and free-space loss is the better estimate. Use two-ray only for the long, over-ground far field.
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