Compute the received power of a radio link travelling through free space with the Friis transmission equation. Adjust the transmit power, antenna gains, frequency and distance to see the free-space path loss, received power and link margin update in real time, and design a wireless link budget from Wi-Fi to satellite communications.
Parameters
Transmit power P_tx
W
Power the transmitter feeds into the antenna
Transmit antenna gain G_tx
dBi
How tightly the transmit antenna focuses power
Receive antenna gain G_rx
dBi
How well the receive antenna captures the signal
Frequency f
MHz
Radio frequency. Higher frequency means more path loss
Link distance d
km
Distance between the transmit and receive antennas
Results
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Wavelength λ (m)
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Free-space path loss (dB)
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Transmit power (dBm)
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Received power (dBm)
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Received power (W)
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Link margin (dB)
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Radio link — wave-propagation animation
A spherical wavefront expands from the transmit antenna on the left, travels across the distance d and reaches the receive antenna on the right. The brightness of the wavefronts shows the signal fading, and the bar at the bottom shows the link budget (transmit power + gains − path loss = received power).
The Friis transmission equation (decibel form). Every quantity is in decibels (power in dBm, gains and losses in dB). Distance d in km, frequency f in MHz. The free-space path loss FSPL rises with both distance and frequency.
Converting received power in dBm back to watts, and the link margin M. P_sens is the minimum receiver sensitivity (a representative −90 dBm in this tool).
What is the Friis Transmission Equation?
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What exactly is the "Friis transmission equation"? I heard it comes up whenever people talk about Wi-Fi and radio.
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In plain terms, it is the equation that calculates "of the power that leaves the transmitter, how much actually arrives at the receiver". Harald Friis published it in 1946. Every wireless link — your phone, a Wi-Fi router, TV broadcasting, even a Mars rover — faces the same basic accounting problem: only a fraction of the power sent out ever arrives. The Friis equation predicts that fraction for the idealised case of free space: a clear path with no obstacles, no reflections and no atmospheric absorption.
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Even in an ideal space with nothing in the way, the signal still gets weaker?
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That is the most counter-intuitive part of the equation. Even with nothing in the way, the signal weakens dramatically with distance. We call this "free-space path loss" (FSPL). The transmitting antenna spreads its power over an ever-expanding spherical wavefront, like an inflating balloon. The receiving antenna only catches a tiny patch of that swelling sphere. The sphere's surface area grows with the square of distance, so the receiver's share falls with the square of distance. Try doubling the "link distance" slider on the left — the received power should drop to exactly a quarter, that is −6 dB.
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Raising the frequency also increases the path loss. Why is that — it is different from distance, isn't it?
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It is a subtle reason. A higher frequency means a shorter wavelength. And the effective "catching area" of an antenna of fixed gain is proportional to the wavelength squared. So at higher frequencies the receiving antenna is, in effect, a smaller bucket. With the same 12 dBi gain, the area you can capture at 2.4 GHz and at 24 GHz differs by orders of magnitude. That is why the FSPL formula contains a frequency term as well as a distance term. You can see that upward-sloping curve on the "free-space path loss vs frequency" chart below.
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Can I claw that loss back by raising the transmit power or the antenna gains?
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Yes — that is the whole idea of a link budget. Received power = transmit power + transmit gain + receive gain − path loss. Gain measures how well an antenna concentrates power in the wanted direction instead of wasting it everywhere; focus it to a point and that much more reaches the receiver. Engineers do the whole calculation in decibels, because then gains simply add and losses simply subtract, turning the link budget into a plain arithmetic table. A parabolic dish has a gain above 30 dBi precisely because that "focusing" is how it fights path loss.
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So what is the "link margin" that comes out at the end actually telling me?
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Link margin is how far the received power sits above the minimum the receiver needs — its sensitivity. If the margin is below zero, the link does not close. But sitting exactly at zero is dangerous. Real signals are attenuated by rain, shaken by fading, or weakened when an antenna drifts slightly off-aim. So engineers design with 10 dB or more of margin, and 20 dB or more for critical links like satellite. A healthy margin is the insurance that keeps the link working through bad weather and small misalignments.
Frequently Asked Questions
The Friis transmission equation predicts the received power of a radio link in free space — an ideal medium with no obstacles, reflections or atmospheric absorption. It was published by Harald Friis in 1946. In decibels it reads P_rx = P_tx + G_tx + G_rx − FSPL: simply add the transmit power and the two antenna gains, then subtract the free-space path loss FSPL to get the received power. It is the starting point for designing every wireless link, from a Wi-Fi router to a deep-space probe.
A transmitting antenna spreads its power over an expanding spherical wavefront, and the receiving antenna intercepts only a tiny patch of that sphere. The sphere's surface area grows with the square of distance, so the received power falls with the square of distance — double the range and received power drops to a quarter. FSPL also rises with frequency: a higher frequency means a shorter wavelength, and the effective catching area of a fixed-gain antenna is proportional to wavelength squared, so at higher frequencies the receiving antenna is effectively a smaller bucket. In the standard decibel form (distance in km, frequency in MHz), FSPL = 20*log10(d) + 20*log10(f) + 32.44 dB.
Link margin is how far the received power sits above the minimum the receiver needs to work. This tool uses a representative sensitivity of −90 dBm, so linkMargin = P_rx − (−90) dB. A margin below zero means the link does not close. Because real signals are weakened by rain, fading, antenna misalignment and temperature drift, engineers typically aim for at least 10 dB of margin, and 20 dB or more for satellite or critical links.
Power ratios span many orders of magnitude, so handling them as linear watts makes the multiplication and division clumsy. Converting to decibels (a logarithmic scale) turns every gain into an addition and every loss into a subtraction, so the link budget becomes simple arithmetic: add a 40 dBm transmit power and the antenna gains, subtract a 120 dB path loss, and you have the received power. To convert received power back to watts, use P[W] = 10^((P_dBm − 30)/10).
Real-World Applications
Wi-Fi and wireless LAN design: Placing access points in an office or home is exactly the world of the Friis equation. At the same distance, 2.4 GHz and 5 GHz differ by about 6 dB of path loss, so 5 GHz attenuates more and reaches shorter distances. Because access-point transmit power is capped by regulation, designers set coverage from the antenna gain, the mounting position and the "wall penetration loss". This tool's free-space calculation is an idealised value with no obstacles; in a real indoor space, a single wall adds several dB to over ten dB of extra loss.
Satellite communications and GPS: A geostationary satellite sits about 36,000 km away, and feeding that into the Friis equation gives a path loss well over 200 dB. To close that link, ground stations use high-gain parabolic dishes several metres across, and the satellite illuminates the Earth with a highly directional antenna. A GPS receiver can decode signals as faint as around −130 dBm only because it gains processing gain from the spreading code; the link-budget logic itself is built on the calculation this tool performs.
Cellular and 5G networks: In base-station cell planning, the cell radius is set so the received power at the cell edge does not fall below the receiver sensitivity. The millimetre waves used in 5G (the 28 GHz band, for example) are high in frequency, so — exactly as the Friis equation predicts — the free-space path loss is very large, the cells become small, and base stations must be packed densely. Lower bands (such as 700 MHz) have less loss and cover wider areas. The difference in "reach" between bands is explained directly by the frequency term of FSPL.
Radar and space exploration: Telemetry from a Mars probe travels hundreds of millions of kilometres, so the path loss reaches astronomical values. NASA's Deep Space Network uses 70 m dishes precisely to claw back, with receive gain, some of the staggering loss the Friis equation predicts. The radar equation is the Friis equation extended to a round trip (transmit → target → receive), so the thinking behind this tool feeds directly into radar link budgets too.
Common Misconceptions and Pitfalls
The biggest misconception is assuming the Friis equation value is the actual received power. The Friis transmission equation is strictly a free-space value — an ideal space with no obstacles, no reflections and no atmosphere. In a real environment you must add shadowing and diffraction loss from buildings, terrain and trees, multipath fading from ground reflections, and absorption by rain and atmospheric gases (significant above about 10 GHz). Indoors, one wall adds several dB and a concrete wall over ten dB. Use this tool's result as an upper-bound estimate — "it can only get worse than this, almost never better" — and always add extra margin for the real environment.
Next, confusing dBm, dBi and dB. This is the single most common mistake for beginners. dBm is an absolute power level (an absolute quantity referenced to 1 mW), dBi is antenna gain referenced to an isotropic antenna, and dB is a pure ratio (a loss or a difference). The Friis equation P_rx[dBm] = P_tx[dBm] + G_tx[dBi] + G_rx[dBi] − FSPL[dB] has the structure of adding and subtracting relative quantities to an absolute quantity to get an absolute quantity. Mix up the units and the orders of magnitude no longer line up. Forgetting the ×1000 (W → mW) in the transmit-power conversion 10·log10(P[W]×1000) is also a very common error.
Finally, jumping to the conclusion that higher frequency is always worse. It is true that the frequency term of the Friis equation makes FSPL larger and looks unfavourable at higher frequencies. But that holds only under the assumption of constant gain. For an antenna with a fixed physical aperture (such as a parabolic dish), gain rises with frequency, so if both ends use dishes of the same diameter the frequency penalty is cancelled by the gain advantage — and higher frequency can even win. When you use the Friis equation, always be aware of whether you are comparing at constant gain or at constant aperture. This tool treats gain as an independent input, so it is fundamentally a constant-gain comparison.
How to Use
Enter transmit power in watts or dBm using txPowerNum/txPowerRange sliders.
Set transmit antenna gain (dBi) and receive antenna gain (dBi) via txGainNum/rxGainNum controls.
Specify operating frequency in MHz or GHz using frequencyNum/frequencyRange.
Read Wavelength λ, Free-space path loss (dB), and Received power (dBm/W) in real-time output fields.
Monitor Link margin (dB) to assess fade headroom above receiver sensitivity threshold.
Worked Example
802.11n WiFi link at 2.4 GHz: Transmit power 20 dBm (100 mW), transmit antenna gain 2 dBi, receive antenna gain 2 dBi, distance 50 m. Wavelength λ = 0.125 m. Free-space path loss = 80.0 dB. Received power = 20 + 2 + 2 - 80.0 = -56 dBm (-3.98 µW). If receiver sensitivity is -70 dBm, link margin = 14 dB (adequate for 1–2 m/s fading margin).
Practical Notes
Path loss doubles (6 dB increase) when distance quadruples; verify operating range against antenna gain and transmit power budget.
Terrestrial microwave links (5–28 GHz) benefit from high-gain parabolic dishes (35+ dBi); WiFi and cellular use omnidirectional or sectoral antennas (2–15 dBi).
Fade margin below 3 dB indicates unreliable operation in rain or obstruction; add power, gain, or relocate for critical links.
Frequency scaling: doubling frequency increases path loss by 6.02 dB; low-band 700 MHz cellular reaches farther than 2.6 GHz with identical power/gain.