Friis Transmission Equation Calculator

Compute received power in a free-space radio link from transmit power, transmit and receive antenna gains, link distance, and frequency using the Friis transmission equation.

🛰️ Friis Transmission Equation Calculator
Transmit power (Pt)20 dBm
dBm
-1050
Transmit antenna gain (Gt)10 dBi
dBi
-1045
Receive antenna gain (Gr)15 dBi
dBi
-1045
Distance (d)5 km
km
0.1100
Frequency (f)2.4 GHz
GHz
0.140
Received power (Pr)
—
Free-space path loss (FSPL)
—
Received power (mW)
—
Step-by-step working

🛰️ What is the Friis Transmission Equation?

The Friis transmission equation predicts the power received by an antenna in a free-space radio link, given the transmit power, the gains of the transmitting and receiving antennas, and the distance and frequency that together determine the free-space path loss between them. First published by Harald T. Friis in 1946, it remains the foundational equation for radio frequency (RF) link budget analysis, the calculation every wireless system designer performs to check whether a link will actually work before building it.

RF and communications engineers use the Friis equation at every scale. A WiFi or Bluetooth designer estimates received signal strength at the edge of a coverage area to confirm it stays above the receiver's sensitivity threshold. A satellite communications engineer computes the downlink budget for a geostationary link, where distances of tens of thousands of kilometers produce enormous path loss that only high-gain dish antennas and careful power budgeting can overcome. A point-to-point microwave backhaul engineer sizes antenna gains and transmit power to close a multi-kilometer terrestrial link with an adequate safety margin against rain fade and multipath.

A common misconception is that the Friis equation accounts for real-world obstacles like buildings, terrain, foliage, or weather. In reality, it strictly models idealized free-space (line-of-sight) propagation, so the received power it predicts is a best-case ceiling. Real links typically need additional link margin, often 10 to 20 dB or more, to remain reliable once real-world losses like fading, multipath, and atmospheric absorption are accounted for.

This calculator takes the transmit power, both antenna gains, the link distance, and the operating frequency, and returns the received power in dBm and milliwatts, the free-space path loss in dB, full step-by-step working, and a chart showing how received power falls off as distance increases for the same power and gains.

📐 Formula

Pr(dBm)  =  Pt + Gt + Gr − FSPL
FSPL(dB) = 20×log₁₀(dkm) + 20×log₁₀(fMHz) + 32.44, with fMHz = fGHz × 1000
Pt = transmit power (dBm), Gt = transmit antenna gain (dBi), Gr = receive antenna gain (dBi)
d = distance between antennas (km), f = operating frequency (GHz)
Example: Pt = 20 dBm, Gt = 10 dBi, Gr = 15 dBi, d = 5 km, f = 2.4 GHz → FSPL ≈ 114.02 dB, Pr ≈ −69.02 dBm.

📖 How to Use This Calculator

Steps

1
Enter the transmit power and antenna gains. Type the transmit power Pt in dBm and the transmit and receive antenna gains Gt and Gr in dBi.
2
Enter the link distance and frequency. Type the distance between the antennas in kilometers and the operating frequency in GHz.
3
Read the received power and free-space path loss. See the received power Pr, the free-space path loss FSPL, and a chart of received power versus distance.

💡 Example Calculations

Example 1 — Short-Range WiFi-Style Link

Pt = 20 dBm, Gt = 10 dBi, Gr = 15 dBi, d = 5 km, f = 2.4 GHz

1
fMHz = 2.4 × 1000 = 2400 MHz
2
FSPL = 20×log₁₀(5) + 20×log₁₀(2400) + 32.44 = 13.98 + 67.60 + 32.44 ≈ 114.02 dB
3
Pr = 20 + 10 + 15 − 114.02 = −69.02 dBm
Pr ≈ −69.02 dBm, well above a typical WiFi receiver's −80 to −90 dBm sensitivity
Try this example →

Example 2 — Geostationary Satellite Downlink

Pt = 30 dBm, Gt = 25 dBi, Gr = 30 dBi, d = 40,000 km, f = 4 GHz

1
fMHz = 4 × 1000 = 4000 MHz
2
FSPL = 20×log₁₀(40000) + 20×log₁₀(4000) + 32.44 = 92.04 + 72.04 + 32.44 ≈ 196.52 dB
3
Pr = 30 + 25 + 30 − 196.52 = −111.52 dBm
Pr ≈ −111.52 dBm, illustrating why satellite links need high-gain dish antennas and low-noise receivers to close reliably over such enormous distances
Try this example →

Example 3 — Short Point-to-Point Microwave Link

Pt = 15 dBm, Gt = 6 dBi, Gr = 6 dBi, d = 1 km, f = 5.8 GHz

1
fMHz = 5.8 × 1000 = 5800 MHz
2
FSPL = 20×log₁₀(1) + 20×log₁₀(5800) + 32.44 = 0 + 75.27 + 32.44 ≈ 107.71 dB
3
Pr = 15 + 6 + 6 − 107.71 = −80.71 dBm
Pr ≈ −80.71 dBm, a typical result for a short 5.8 GHz backhaul link with modest antenna gains
Try this example →

❓ Frequently Asked Questions

What is the Friis transmission equation?+
The Friis transmission equation predicts the power received by an antenna in a free-space radio link from the transmit power, the gains of both the transmitting and receiving antennas, and the free-space path loss between them: Pr(dBm) = Pt + Gt + Gr minus FSPL, with every term expressed in decibels.
How do you calculate free-space path loss (FSPL)?+
FSPL(dB) = 20 times log10(distance in km) + 20 times log10(frequency in MHz) + 32.44, a practical decibel form of the Friis equation that works directly with distance in kilometers and frequency in megahertz without unit conversion by hand.
How does distance affect received power?+
Received power falls off with the square of distance in free space, so doubling the link distance increases free-space path loss by 20 times log10(2), about 6.02 dB, and correspondingly reduces received power by the same 6.02 dB, regardless of the frequency or antenna gains involved.
How does frequency affect received power for fixed antenna gains?+
For fixed antenna gains in dBi, higher frequency means more free-space path loss, doubling the frequency adds about 6.02 dB of FSPL and reduces received power by the same amount. This happens because the antenna gain-aperture relationship keeps effective aperture, not gain, constant as wavelength shrinks.
What antenna gain unit does the Friis equation use?+
The Friis equation as used here expects both Gt and Gr in dBi, decibels relative to an isotropic radiator, the standard unit on most antenna datasheets. If a gain is given in dBd (relative to a half-wave dipole), add 2.15 dB to convert to dBi first.
Does the Friis equation account for obstacles, rain, or reflections?+
No, the Friis transmission equation assumes ideal free-space (line-of-sight) propagation with no obstructions, multipath reflections, or atmospheric absorption. Real-world links typically experience additional losses beyond FSPL, so the calculated Pr represents a best-case, idealized received power.
How do I know if my received power is enough for a working link?+
Compare the calculated Pr against your receiver's sensitivity specification, typically a negative dBm value listed on the radio or modem datasheet (for example, minus 90 dBm for many long-range IoT radios). If Pr exceeds the sensitivity threshold by a reasonable margin (a link margin of 10 to 20 dB is common practice), the link should close reliably.
Why does the FSPL formula use the constant 32.44?+
The 32.44 constant absorbs the unit conversions (speed of light, 4-pi geometric spreading factor, and the km/MHz unit choice) needed so that FSPL(dB) can be computed directly from distance in kilometers and frequency in megahertz, without separately converting to meters and hertz and working through the raw (4-pi-d/lambda) squared formula.
What is a typical link budget example using the Friis equation?+
A geostationary satellite downlink at 4 GHz over about 36,000 to 40,000 km of slant range typically shows a free-space path loss around 195 to 197 dB, this calculator's satellite example (30 dBm transmit power, 25 and 30 dBi antenna gains, 40,000 km, 4 GHz) reproduces that order of magnitude directly.
Can I use this calculator for WiFi or Bluetooth link budgets?+
Yes, the same Friis equation applies at any frequency and distance, short indoor WiFi and Bluetooth links (2.4 or 5.8 GHz, tens of meters) just involve much smaller FSPL values than long-range satellite or point-to-point microwave links, giving correspondingly higher received power for the same transmit power and gains.
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What is the Friis transmission equation?

The Friis transmission equation predicts the power received by an antenna in a free-space radio link from the transmit power, the gains of both the transmitting and receiving antennas, and the free-space path loss between them: Pr(dBm) = Pt + Gt + Gr minus FSPL, with every term expressed in decibels.

How do you calculate free-space path loss (FSPL)?

FSPL(dB) = 20 times log10(distance in km) + 20 times log10(frequency in MHz) + 32.44, a practical decibel form of the Friis equation that works directly with distance in kilometers and frequency in megahertz without unit conversion by hand.

How does distance affect received power?

Received power falls off with the square of distance in free space, so doubling the link distance increases free-space path loss by 20 times log10(2), about 6.02 dB, and correspondingly reduces received power by the same 6.02 dB, regardless of the frequency or antenna gains involved.

How does frequency affect received power for fixed antenna gains?

For fixed antenna gains in dBi, higher frequency means more free-space path loss, doubling the frequency adds about 6.02 dB of FSPL and reduces received power by the same amount. This happens because the antenna gain-aperture relationship keeps effective aperture, not gain, constant as wavelength shrinks.

What antenna gain unit does the Friis equation use?

The Friis equation as used here expects both Gt and Gr in dBi, decibels relative to an isotropic radiator, the standard unit on most antenna datasheets. If a gain is given in dBd (relative to a half-wave dipole), add 2.15 dB to convert to dBi first.

Does the Friis equation account for obstacles, rain, or reflections?

No, the Friis transmission equation assumes ideal free-space (line-of-sight) propagation with no obstructions, multipath reflections, or atmospheric absorption. Real-world links typically experience additional losses beyond FSPL, so the calculated Pr represents a best-case, idealized received power.

How do I know if my received power is enough for a working link?

Compare the calculated Pr against your receiver's sensitivity specification, typically a negative dBm value listed on the radio or modem datasheet (for example, minus 90 dBm for many long-range IoT radios). If Pr exceeds the sensitivity threshold by a reasonable margin (a link margin of 10 to 20 dB is common practice), the link should close reliably.

Why does the FSPL formula use the constant 32.44?

The 32.44 constant absorbs the unit conversions (speed of light, 4-pi geometric spreading factor, and the km/MHz unit choice) needed so that FSPL(dB) can be computed directly from distance in kilometers and frequency in megahertz, without separately converting to meters and hertz and working through the raw (4-pi-d/lambda) squared formula.

What is a typical link budget example using the Friis equation?

A geostationary satellite downlink at 4 GHz over about 36,000 to 40,000 km of slant range typically shows a free-space path loss around 195 to 197 dB, this calculator's satellite example (30 dBm transmit power, 25 and 30 dBi antenna gains, 40,000 km, 4 GHz) reproduces that order of magnitude directly.

Can I use this calculator for WiFi or Bluetooth link budgets?

Yes, the same Friis equation applies at any frequency and distance, short indoor WiFi and Bluetooth links (2.4 or 5.8 GHz, tens of meters) just involve much smaller FSPL values than long-range satellite or point-to-point microwave links, giving correspondingly higher received power for the same transmit power and gains.

📌 Quick Tips

💡Free-space path loss grows with the square of both distance and frequency, so doubling either the link distance or the operating frequency adds exactly 6.02 dB of path loss (20 times log10(2)), a useful mental shortcut when comparing candidate frequencies or link ranges.
💡This form of the Friis equation, FSPL(dB) = 20log10(d_km) + 20log10(f_MHz) + 32.44, is the practical decibel version used directly with distance in kilometers and frequency in megahertz, avoiding the need to convert to meters and hertz by hand.
💡The Friis transmission equation assumes free-space (line-of-sight) propagation with no obstructions, reflections, or atmospheric absorption. Real links, especially near the ground or through weather, experience additional losses this equation does not capture, so the result is a best-case (idealized) received power.
💡Received power in dBm converts to linear milliwatts with Pr(mW) = 10 raised to the power of (Pr(dBm) / 10). A typical WiFi receiver sensitivity around minus 70 to minus 90 dBm corresponds to well under a microwatt of actual received power, illustrating how much a radio link amplifies weak signals.
💡Antenna gain must be entered as dBi (relative to an isotropic radiator), the convention this calculator and the standard Friis equation both use. If a datasheet gives gain in dBd (relative to a half-wave dipole), add 2.15 dB to convert it to dBi before entering it here.