RF link budget calculator: free-space path loss, EIRP and range

The free-space path loss between two antennas by ITU-R P.525, the EIRP of the transmitter in dBm, dBW and watts, the received power and the margin over a receiver's sensitivity, the free-space range for that sensitivity, and the field strength and power flux-density at the receiver. The equations are P.525's; the page's tests rebuild every constant P.525 prints from first principles. The defaults are an illustrative 2.4 GHz link over 100 m.

Fig 1 — Received power against distance in free space, falling 20 dB per decade (ITU-R P.525 Eq 5). At 100 m the receiver gets −67.2 dBm, 22.8 dB above the −90 dBm sensitivity; the line meets the sensitivity at 1.38 km.

Fig 2 — The budget step by step, in dB, transmitter on the left. 10.0 dBm out of the transmitter; EIRP 11.5 dBm after the transmit cable and antenna; 80.2 dB of free-space loss; −67.2 dBm at the receiver input, a margin of 22.8 dB over the −90 dBm sensitivity. The row under the columns is the level after each step, in dBm.

Frequency f (MHz)

Distance d (m)

Distance unit

Transmit power Ptx (dBm)

Transmit power unit

Transmit antenna gain Gtx (dBi)

Transmit-side loss Ltx (dB)

Receive antenna gain Grx (dBi)

Receive-side loss Lrx (dB)

Other path losses Lother (dB)

Receiver sensitivity S (dBm)

Free-space path loss L_bf = 20 log(4πd/λ), P.525 Eq 5: 80.20 dB
Same, by P.525 Eq 6 with its rounded 32.4 dB constant: 80.15 dB
EIRP = P_tx + G_tx − L_tx (dBm · dBW · W): 11.50 dBm · −18.50 dBW · 14.1 mW
Received power P_rx = EIRP − L_bf + G_rx − L_rx − L_other: −67.20 dBm · 191 pW
Link margin over the −90.0 dBm sensitivity: +22.80 dB
Range for the sensitivity: distance where the margin reaches 0 dB: 1.38 km
Field strength at 100 m, e = √(30·EIRP)/d, P.525 Eq 1: 6.51 mV/m · 76.3 dB(µV/m)
Power flux-density at 100 m, s = EIRP/(4πd²), P.525 Eq 3: 112 nW/m² · −69.5 dB(W/m²)
Wavelength · effective aperture of an isotropic antenna, P.525 Eq 4: 12.3 cm · 12.0 cm²

How this is calculated

Standard: Recommendation ITU-R P.525-5 (11/2024), Calculation of free-space attenuation (Eq 1–6, 8–11; pp. 1–4); BIPM SI Brochure, 9th edition (c)

$L_{bf} = -10\log_{10}\left(\frac{1}{4\pi d^2}\times\frac{\lambda^2}{4\pi}\right) = 20\log_{10}\left(\frac{4\pi d}{\lambda}\right)\ \text{dB}$: P.525 Equation (5) (p. 3), the free-space basic transmission loss between isotropic antennas: "d and λ are expressed in the same unit". The first factor is the spreading of Eq (3), the second the effective aperture of a receiving isotropic antenna, λ²/4π, of Eq (4). λ = c/f with the exact c = 299 792 458 m/s.
$L_{bf} = 32.4 + 20\log_{10} f + 20\log_{10} d\ \text{dB}, \qquad f\ \text{in MHz},\ d\ \text{in km}$: P.525 Equation (6) (p. 3). With the exact c the constant is 20 log(4π × 10⁹/c) = 32.448 dB; the calculator evaluates Eq (5) and shows Eq (6) beside it.
$\text{EIRP} = P_{tx} - L_{tx} + G_{tx}, \qquad P_{rx} = \text{EIRP} - L_{bf} + G_{rx} - L_{rx} - L_{other}$: Derived. P.525 defines the e.i.r.p. as the "equivalent isotropically radiated power (e.i.r.p.) of the transmitter in the direction of the point in question" (p. 2) but prints no expression for it; the sums add gains stated in dBi to P.525's loss between isotropic antennas. The link margin is P_rx less the sensitivity.
$d_{max} = \frac{\lambda}{4\pi}\,10^{(\text{EIRP} + G_{rx} - L_{rx} - L_{other} - S)/20}$: Derived: Eq (5) inverted for the distance at which P_rx equals the sensitivity S. Each 6.02 dB of margin doubles it.
$e = \frac{\sqrt{30p}}{d}, \qquad s = \frac{e^2}{120\pi} = \frac{p}{4\pi d^2}$: P.525 Equations (1) and (3) (p. 2): r.m.s. field strength e in V/m and power flux-density s in W/m² at d metres from an e.i.r.p. of p watts. Eq (2), the practical form, is e = 173 √p/d in mV/m, kW and km.
$E = P_t - 20\log_{10} d + 74.8, \qquad P_r = E - 20\log_{10} f - 167.2, \qquad S = E - 145.8$: P.525 Equations (8), (9) and (11) (p. 4), with E in dB(µV/m), P in dB(W), f in GHz, d in km and S in dB(W/m²). From Eq (1), (3), (4) and c the constants are 74.77, 167.22 and 145.76.

Assumptions

Free space: in P.525's definition "a perfect vacuum which may be considered of infinite extent in all directions" (p. 1). No ground, atmosphere, obstruction or reflection; an allowance for any of them goes in the other-losses field.
The receiver is in the far field, where the field falls as 1/d: "beyond a distance determined by the size of the source and the wavelength" (P.525 footnote 1).
Antenna gains are in dBi, toward the other end of the link, with matched polarisation. No gain is computed from an antenna's size: P.525 states only the isotropic aperture λ²/4π.
The receive antenna is conjugately matched, as P.525 Eq (9) assumes; any mismatch is entered as a loss.
The field strength is for a linearly polarised wave; P.525 Note 1 replaces e by e√2 for circular polarisation.
One-way propagation; the radar case of P.525 Eq (7) is not computed.

What sets the received power: free-space path loss and EIRP

A link budget follows the signal from the transmitter's output to the receiver's input and adds up what happens to it, in decibels: the loss in the cable to the antenna, the antenna's gain, the loss over the path, the receive antenna's gain, the loss in the cable to the receiver. The path is the large term, and for a clear path it is the free-space path loss. Recommendation ITU-R P.525-5, Calculation of free-space attenuation, is the reference for it, and it says why it is worth having even though no real link runs in a vacuum: "free-space propagation is a fundamental reference for radio-engineering" (p. 1). It defines free space as "a perfect vacuum which may be considered of infinite extent in all directions" (p. 1).

P.525 builds the loss from two factors, both between isotropic antennas. A transmitter radiating p watts equally in all directions spreads them over a sphere, so at distance d the power flux-density is s = p/(4πd²) (Eq 3). A receiving isotropic antenna collects that flux over its effective aperture, which P.525 gives as λ²/4π, so "the power at the output of the receiving isotropic antenna" is the product of the two (Eq 4, p. 3). The free-space basic transmission loss L_bfis the ratio of transmitted to received power in dB, 20 log(4πd/λ) (Eq 5). Nothing is absorbed. The 1/d² is the sphere; the frequency enters only through the receiving aperture, which shrinks as λ². An isotropic antenna at 868 MHz has an effective aperture of 94.9 cm²; at 2.44 GHz, 12.0 cm².

The transmitter side is summarised by the EIRP. P.525 uses it throughout, defined as the "equivalent isotropically radiated power (e.i.r.p.) of the transmitter in the direction of the point in question" (p. 2): the power an isotropic antenna would have to radiate to put the same flux at the receiver. P.525 gives no formula for it, because it is what a gain in dBi means: the transmitter's output, less the loss between it and the antenna, plus the antenna's gain toward the receiver, EIRP = P_tx − L_tx + G_tx. The same reasoning adds the receive antenna's gain to the isotropic received power. So the budget is P_rx = EIRP − L_bf + G_rx − L_rx − L_other, and the link margin is how far P_rx sits above the receiver's sensitivity. The two sums are derived from P.525's definitions; the free-space loss in the middle of them is P.525's own equation.

The free-space path loss formula and its 32.4 dB constant

Eq 5 is the exact form: L_bf = 20 log(4πd/λ), where, in P.525's words, "d and λ are expressed in the same unit" (p. 3). "Equation (5) can also be written using the frequency instead of the wavelength", and P.525 does so as Eq 6, L_bf = 32.4 + 20 log f + 20 log d with f in MHz and d in km. The constant is 20 log(4π × 10⁹/c). With the exact SI speed of light, c = 299 792 458 m/s, it is 32.448 dB, so Eq 6 as printed sits 0.048 dB below Eq 5 at every frequency and distance. The calculator evaluates Eq 5 and shows Eq 6 beside it; the difference is far below anything a link budget can resolve, but it is why two calculators can disagree in the second decimal place.

The constant changes with the units, and this is where most wrong answers come from. P.525's section 4 gives its conversion formulae with f in GHz, and notes that "equations (8) and (10) can be used to derive equation (6)" (p. 4). Doing so gives 92.4 + 20 log f(GHz) + 20 log d(km) from the printed constants (167.2 − 74.8 = 92.4), or 92.45 dB unrounded. With f in MHz and d in metres the constant is −27.55 dB. Every one of P.525's printed constants follows from its Eq 1, 3, 4 and 5, and the page's tests rebuild each from first principles:

P.525 equation	What it converts	Printed	From first principles
Eq (2)	field strength, mV/m, from e.i.r.p. in kW and d in km	173	173.21
Eq (6)	free-space loss, f in MHz, d in km	32.4	32.448
Eq (7)	radar loss, f in MHz, d in km	103.4	103.440
Eq (8)	field strength, dB(µV/m), from Pt in dB(W)	74.8	74.771
Eq (9)	received power from field strength, f in GHz	167.2	167.219
Eq (11)	power flux-density from field strength	145.8	145.763

Each printed value is the first-principles value rounded to the digits shown. Eq 1 and Eq 3 use 120π = 376.99 Ω for the impedance of free space; Eq 9 and the free-space loss itself also depend on c. The radar row, Eq 7, is the loss out to a target and back, "a special case because the signal is subjected to a loss while propagating both from the transmitter to the target and from the target to the receiver" (p. 3), with 40 log d in place of 20 log d. This calculator does not compute it.

Free-space path loss table

Eq 5 at a few common frequencies and distances. Every row rises 20 dB per decade of distance, and 6.02 dB per doubling; every column rises 20 dB per decade of frequency.

Frequency	Wavelength	10 m	100 m	1 km	10 km	100 km
433 MHz	69.2 cm	45.2 dB	65.2 dB	85.2 dB	105.2 dB	125.2 dB
868 MHz	34.5 cm	51.2 dB	71.2 dB	91.2 dB	111.2 dB	131.2 dB
2.44 GHz	12.3 cm	60.2 dB	80.2 dB	100.2 dB	120.2 dB	140.2 dB
5.8 GHz	5.2 cm	67.7 dB	87.7 dB	107.7 dB	127.7 dB	147.7 dB
12 GHz	2.5 cm	74.0 dB	94.0 dB	114.0 dB	134.0 dB	154.0 dB

Read across from 100 m to 1 km and the loss rises by 20 dB, which is 100 times less power. That is the case for counting every dB elsewhere in the budget: 6 dB anywhere in it, in antenna gain, cable loss or sensitivity, is worth a factor of two in free-space range.

Worked example: a 2.4 GHz link over 100 m (illustrative)

P.525 prints no numeric example, so the calculator's defaults are an illustrative short-range link, not one taken from a source: 10 dBm out of the transmitter, half a dB of cable or matching loss at each end, 2 dBi antennas at both ends, 100 m apart, at 2.44 GHz, into a receiver with a sensitivity of −90 dBm.

λ         c / f = 299 792 458 / 2.44 × 10⁹           = 12.3 cm
Lbf       20 log(4π × 100 / 0.1229)                  = 80.20 dB
          Eq 6: 32.4 + 20 log 2440 + 20 log 0.1      = 80.15 dB
EIRP      10 dBm + 2 dBi − 0.5 dB                    = 11.5 dBm
          in dBW, and in watts                       = −18.5 dBW, 14.1 mW
Prx       11.5 − 80.20 + 2 − 0.5                     = −67.20 dBm
margin    −67.20 − (−90)                             = 22.80 dB
range     100 m × 10^(22.80/20)                      = 1.38 km

The received power is −67.2 dBm, a margin of 22.8 dB over the sensitivity, and in free space the link would reach 1.38 kmbefore the margin ran out. Eq 6 with its rounded constant gives a loss 0.048 dB lower. Figure 1 is the received power along the whole path, falling 20 dB per decade; Figure 2 is the same budget as a waterfall, where the free-space loss dwarfs every other term and the cable losses are barely visible.

The −90 dBm is not arbitrary. A receiver's sensitivity is its noise floor plus the signal-to-noise ratio its demodulator needs, and the floor is kT₀ in the noise bandwidth plus the noise figure. In 1 MHz, kT₀B is −114.0 dBm; with an illustrative 6 dB noise figure the floor is −108.0 dBm, and a −90 dBm sensitivity means the demodulator needs 18.0 dB of SNR. Thenoise figure calculator does that arithmetic from a real receiver chain. The floor rises 10 log B with the noise bandwidth, so a receiver mode with ten times the bandwidth needs 10 dB more signal for the same SNR.

Worked example: long range at 868 MHz (illustrative)

The same budget at 868 MHz, 14 dBm out, the same 2 dBi antennas and half-dB losses, 10 km apart, into an illustrative narrow-band receiver of −120 dBm sensitivity. The free-space loss is 111.22 dB, the received power −94.2 dBm and the margin 25.8 dB, which in free space would stretch to 195 km. Move the same link to 2.44 GHz and the loss rises by 20 log(2440/868) = 8.98 dB: the margin at 10 km falls to 16.8 dB. With fixed-gain antennas at both ends, a lower frequency buys range, because the receiving aperture is larger, not because the signal travels further.

Those ranges are free-space figures. They are what a vacuum with no ground in it would give, which is not where a 10 km link runs; what the ground, terrain and atmosphere do to it is outside P.525 and outside this page. Use the other-losses field to hold an allowance for them.

Worked example: a satellite-length path (illustrative)

Free space is closest to true over a path that is nearly all vacuum. An illustrative 36 000 km downlink at 12 GHz loses 205.16 dB to free space alone. With 100 W out (50 dBm), 1 dB of feed loss and a 40 dBi transmit antenna the EIRP is 89 dBm, or 59 dBW; a 35 dBi receive dish with 1 dB of feed loss then delivers −82.2 dBm, and against a −100 dBm sensitivity the margin is 17.8 dB. The flux-density at the ground is −103.1 dB(W/m²). P.525's section 4 works in dB(W), which is dBm − 30; the calculator gives the EIRP in both, and in watts.

Field strength and power flux-density at a distance

For a transmitter serving many receivers, P.525 works in field strength rather than loss: "If there is a transmitter serving several randomly-distributed receivers (broadcasting, mobile service), the electric field is calculated at a point located at some appropriate distance from the transmitter" (p. 2), by Eq 1, e = √(30p)/d, with e the r.m.s. field in V/m, p the e.i.r.p. in watts and d in metres. "Equation (1) is often replaced by equation (2) which uses practical units", e_mV/m = 173 √p_kW/d_km: 1 kW of EIRP at 1 km is 173.2 mV/m. The power flux-density follows from Eq 3, s = e²/120π = p/(4πd²).

In decibels, section 4 gives the field strength in dB(µV/m) from an isotropically transmitted power in dB(W) as E = P_t − 20 log d + 74.8 (Eq 8, d in km), and the flux-density as S = E − 145.8 (Eq 11). The calculator uses the EIRP for P_t, which is what Eq 1 takes. For the 2.4 GHz example, 11.5 dBm at 100 m is 6.5 mV/m, or 76.27 dB(µV/m); Eq 8 with its rounded constant gives 76.30. Two caveats come with these equations in P.525's notes. Eq 1 is for a linearly polarised wave: for elliptical polarisation e becomes √(e_x² + e_y²), and "e should be replaced by e√2 in the case of circular polarization" (Note 1, p. 2). And an antenna at ground level over a plane, perfectly conducting ground radiates into half the space, so "the power flux-density for a given radiated power is doubled, as compared with an antenna in free space" (Note 2, p. 2).

Range for a sensitivity: what each dB of margin buys

The range the calculator reports is Eq 5 inverted: the distance at which the margin falls to zero. Because the loss rises 20 log d, every 20 dB of margin is a factor of ten in distance and every 6.02 dB a factor of two, whichever term the dB comes from.

Margin at d	Free-space range ÷ d
1 dB	1.12
3 dB	1.41
6 dB	2.00
10 dB	3.16
20 dB	10.00
30 dB	31.62

The same table read the other way is the cost of an allowance: hold 10 dB in reserve for fading or obstructions and the free-space range falls to 0.32 of what it was.

Antenna gain: why this page does not compute it from size

Antenna gain enters the budget as a number in dBi, taken from the antenna's datasheet in the direction of the link. The calculator does not derive it from an antenna's physical size. P.525 states only the effective aperture of an isotropic antenna, λ²/4π (Eq 4); it gives no relation between a real antenna's gain and its aperture, and no other document in this site's reference library does. A formula the page cannot cite is one it does not use. What P.525 does make clear is the reference the dBi figure is measured against: every one of its point-to-point equations is "between isotropic antennas" (p. 3), and an antenna of 0 dBi is that antenna.

Where the free-space model stops being valid

Nothing but vacuum. P.525's free space is "a perfect vacuum which may be considered of infinite extent in all directions" (p. 1). There is no ground, no atmosphere, no rain, no wall and no second path by reflection. Its Note 2 deals with one case of ground, an antenna at ground level over a perfect plane, and points to Recommendations ITU-R P.368 and P.341 as where that is included. Any other effect on a real path is outside this calculator; the other-losses field is where an allowance goes, and P.525 gives no values for one.

Far field only. The free-space formulas assume the field falls as 1/d. P.525's footnote 1 quotes the electrotechnical vocabulary's definition, under which that holds "beyond a distance determined by the size of the source and the wavelength" (p. 1). P.525 gives no number for that distance; the calculator notes when the path is shorter than one wavelength, and Eq 5 itself goes to 0 dB at d = λ/4π, where it plainly no longer describes anything physical.

Gains in the direction of the link, and matched. The EIRP is "in the direction of the point in question" (p. 2), so a gain is the antenna's gain toward the other end, not its peak. Eq 9's received power is through "a conjugately matched isotropic receiving antenna" (p. 4); a mismatch between antenna and cable is an extra loss, which the VSWR and return loss calculator converts from a VSWR. Polarisation is assumed to match at both ends.

One-way links. A radar sees the loss twice and goes as 40 log d (Eq 7). This calculator is the one-way case.

Common link budget mistakes

Using Eq 6's constant with the wrong units. 32.4 is for MHz and km; with f in GHz and d in km it is 92.4. Putting 2.44 into the MHz form for the 100 m example gives a loss 60 dB too low; putting 2440 into the GHz form gives 140.1 dB instead of 80.1 dB.
Mixing dBm and dBW. They differ by 30 dB: 11.5 dBm is −18.5 dBW. P.525's section 4 works in dB(W).
Leaving out the cable. Loss between the transmitter and its antenna comes straight off the EIRP, and loss between the receive antenna and the receiver straight off the received power. Take the cable's loss at the link frequency from its datasheet; thecoax impedance calculator shows how a line's geometry sets its impedance and conductor loss.
Using the antenna's peak gain when the link is off its main lobe. The EIRP is in the direction of the receiver.
Treating the free-space range as the range. It is the range in a vacuum. Hold an allowance in the other-losses field for whatever the real path adds.
Quoting a sensitivity without its conditions. The same receiver's sensitivity changes with data rate, bandwidth and the error rate it is specified at; use the figure for the mode the link actually runs.
Adding powers in dB. The budget adds gains and losses in dB to one power level; two powers add as watts. ThedB calculator converts.