Friis Transmission Equation Calculator
Calculate ideal free-space RF received power, required transmit power, maximum distance, required antenna gain and link efficiency using the Friis transmission equation.
RF-012 is an ideal received-power tool. Cable loss, receiver sensitivity, fade margin, atmospheric loss, terrain and complete link-budget terms belong to the RF Link Budget, FSPL and Coaxial Cable Loss calculators.
Engineering tool
Friis Transmission Equation Calculator
Calculate ideal RF received power, required transmit power, maximum distance, required antenna gain and compare ideal free-space RF links.
Result console
- Transmit Power
- 1 W
- Transmit Power dBm
- 30 dBm
- Received Power
- 98.809612 pW
- Received Power dBm
- -70.052008 dBm
- Required Tx Power
- Not required
- Required Tx Power dBm
- Not required
- Maximum Distance
- Not required
- Required Total Antenna Gain
- Not required
- Required Equal Antenna Gain
- Not required
- Required Missing Antenna Gain
- Not required
- FSPL
- 100.052008 dB
- Wavelength
- 12.491352 cm
- Frequency
- 2.4 GHz
- Distance
- 1 km
- Received Power Ratio
- 9.880961e-11
- Ideal Link Efficiency
- 9.880961e-9%
- Formula Used
- Pr(dBm) = Pt(dBm) + Gt(dBi) + Gr(dBi) - FSPL(dB)
Friis transmission equation assumes ideal free-space line-of-sight propagation. It does not include cable loss, mismatch loss, atmospheric loss, rain fade, shadowing, multipath, terrain or receiver sensitivity.
Formula reference
Friis Transmission Equation
Friis can be evaluated in linear power form or in dB link form. The dB form is usually easier for RF engineering calculations.
Pr = Pt × Gt × Gr × (λ / (4πR))²λ = c / fFSPL(dB) = 20log10(4πR / λ)Pr(dBm) = Pt(dBm) + Gt(dBi) + Gr(dBi) - FSPL(dB)Pt(dBm) = Pr(dBm) + FSPL(dB) - Gt(dBi) - Gr(dBi)Gt + Gr = Pr(dBm) - Pt(dBm) + FSPL(dB)Variable definitions
- Pr
- received power
- Pt
- transmit power
- Gt
- transmit antenna gain
- Gr
- receive antenna gain
- λ
- wavelength
- R
- distance between antennas
- c
- speed of light, 299,792,458 m/s
- f
- frequency
- FSPL
- free-space path loss
Worked Examples
1 W, 2.4 GHz, 1 km, 0 dBi antennas
FSPL is about 100.05 dB, so received power is about -70.05 dBm.
100 mW, 915 MHz, 100 m
With 0 dBi antennas, ideal received power is about -51.68 dBm.
30 dBm at 433 MHz
At 100 m with 0 dBi antennas, ideal received power is about -35.17 dBm.
5.8 GHz directional antennas
30 dBm with 15 dBi antennas at both ends over 2 km gives about -53.74 dBm ideal received power.
Required transmit power
To receive -80 dBm at 2.4 GHz over 1 km with 10 dBi antennas at both ends, required transmit power is about 0.05 dBm.
Maximum distance
30 dBm at 915 MHz with 0 dBi antennas can ideally reach about 8.24 km before falling to -80 dBm.
Required antenna gain
At 2.4 GHz over 10 km, 30 dBm transmit power and -80 dBm target require about 10.05 dBi total antenna gain.
Compare links
A 433 MHz link at 100 m is stronger than a 915 MHz link at the same distance and antenna gains because FSPL is lower.
Higher antenna gain
Adding 10 dBi at both antennas increases ideal received power by 20 dB.
Distance scaling
Doubling distance increases free-space path loss by about 6.02 dB.
Engineering Notes
- Friis equation estimates ideal received power in free space.
- Line-of-sight propagation is assumed.
- Antenna gains are referenced to isotropic antennas in dBi.
- Distance and frequency determine the free-space path loss term.
- Higher frequency gives lower received power for the same distance and antenna gains.
- Antenna far-field conditions must be valid.
- Cable loss is not included.
- Atmospheric loss, rain fade, shadowing, terrain and multipath are not included.
- Real RF links often perform worse than the ideal Friis result.
- Use RF-005 when a complete link budget with losses and receiver sensitivity is required.
Common Mistakes
- Treating Friis as a complete link budget.
- Ignoring antenna gain or entering gain in the wrong sign.
- Mixing meters, kilometers and miles.
- Trying to include cable loss inside the Friis equation.
- Ignoring far-field requirements.
- Assuming ideal free-space line of sight exists in real deployments.
- Forgetting that received power is not receiver sensitivity.
- Ignoring polarization, mismatch and antenna pointing.
Support reference
FAQ
What is Friis transmission equation?
Friis transmission equation estimates ideal received RF power in free space from transmit power, transmit antenna gain, receive antenna gain, wavelength and distance.
How do I calculate received RF power?
In dB form, use Pr(dBm) = Pt(dBm) + Gt(dBi) + Gr(dBi) - FSPL(dB), where FSPL is the ideal free-space path loss.
What assumptions does Friis make?
Friis assumes free-space line-of-sight propagation, far-field antennas, matched polarization, matched impedance, no cable loss, no atmospheric loss and no multipath.
Why is received power lower at higher frequency?
For the same distance and antenna gains, wavelength decreases as frequency increases, so the Friis spreading term reduces received power.
Does Friis include cable loss?
No. Cable loss is not part of the ideal Friis equation. Use the Coaxial Cable Loss Calculator or Link Budget Calculator for cable loss.
Does Friis include atmospheric loss?
No. Atmospheric absorption, rain fade, foliage, buildings and terrain are outside this ideal free-space calculation.
How is Friis different from link budget?
Friis calculates ideal received power from free-space spreading and antenna gains. A full link budget also includes cable loss, other losses, sensitivity and margin.
When should I use Friis?
Use Friis for ideal free-space received-power estimates, sanity checks, antenna gain studies and early RF link exploration under line-of-sight assumptions.
What is FSPL in Friis equation?
FSPL is the free-space spreading loss term equal to 20log10(4πR / λ), or equivalently 20log10(4πRf / c).
Can Friis predict real wireless range?
Friis can provide an ideal upper-bound estimate, but real range needs a link budget and field validation.
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Future Engineering Guide Topics
Friis Transmission Equation Explained
In_DevelopmentRF Link Design
In_DevelopmentFree Space Propagation
In_DevelopmentAntenna Gain
In_DevelopmentDisclaimer
This calculator provides ideal free-space Friis equation estimates. Real RF systems should be verified with full link budgets, measured antenna data, cable loss, receiver sensitivity, environmental assumptions and field testing.