HomeCalculatorsElectricalRF & MicrowaveFree-Space Path Loss Calculator
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Free-Space Path Loss Calculator

Compute free-space path loss FSPL = 20·log10(d·f) + 20·log10(4π/c) from distance and frequency, with optional antenna gains. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 3/3 declared partitions (isotropic, with-gains, invalid-domain) · Matrix
Known limitations
  • Free-space isotropic model; path_loss_dB is antenna-adjusted link loss (FSPL − Gt − Gr)
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Free-space path loss and optional antenna-adjusted link loss from distance and frequency.
Scope
Ideal free space; isotropic reference for FSPL.
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
4/4 property · digest 486d3a52cd93
Legacy regression
10/10 tests · Production surface contract 4/4
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. CVP-UI-01: canonical SI is the only calculation source. Mixed share URLs (d_m + fsplDInput without fsplDUnit) must still yield FSPL. Live Chromium session is npm run test:fspl-live-e2e — not executed inside this SSR/REST/MCP probe.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
2/2 golden · 4/4 CVP boundary · 3/3 invalid · 4/4 property · 2/2 cross-interface · 4/4 CVP contract · Manifest
Sources
  • Friis transmission equation — Free-space path loss form
  • ITU-R P.525-5 (11/2024), Calculation of free-space attenuation — Free-space basic transmission loss
Sources
Evidence
2 legacy golden · 4 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 3/3 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

FSPLFSPL = 20·log10(d) + 20·log10(f) + 20·log10(4π/c)
Antenna-adjusted link lossAAL = FSPL − Gt − Gr
iIdeal free-space Friis model. No atmosphere, multipath, diffraction, or cable loss. Friis assumes far-field separation.

How to use

1

Enter distance

Page UI accepts m/km. The calculation and share URL always use metres (d_m).

2

Enter frequency

Page UI accepts Hz/kHz/MHz/GHz. The calculation and share URL always use hertz (f_Hz).

3

Optional gains

Isotropic-equivalent antenna gains in dBi. These do not change FSPL; they produce antenna-adjusted link loss.

Example calculations

Common configurations with formula and result.

ϟ

1 km · 2.4 GHz

d=1000 m · f=2.4 GHz · isotropic

FSPL
≈ 100.05 dB
ϟ

With 6 dBi antennas

Gt=Gr=6 dBi

AAL = FSPL − 12
≈ 88.05 dB antenna-adjusted link loss
ϟ

Wavelength

λ = c/f at 2.4 GHz

λ = c/f
≈ 0.1249 m

Free-Space Path Loss calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-08

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
Free-space path loss (FSPL) is the isotropic-reference loss in free space: FSPL_dB = 20·log10(d_m) + 20·log10(f_Hz) + 20·log10(4π/c). Optional gains Gt and Gr yield antenna-adjusted link loss: path_loss_dB = FSPL − Gt − Gr. Share URLs use SI d_m and f_Hz as the only calculation source.
What it calculates
Free-space path loss and optional antenna-adjusted link loss from distance and frequency.
Inputs
  • d_m > 0 — distance (m)
  • f_Hz > 0 — frequency (Hz)
  • Optional Gt_dBi, Gr_dBi (default 0)
Outputs
  • fspl_dB, path_loss_dB (antenna-adjusted link loss), wavelength_m, d_m, f_Hz, Gt_dBi, Gr_dBi
Formula
FSPL_dB=20·log10(d_m)+20·log10(f_Hz)+20·log10(4π/c); path_loss_dB=FSPL−Gt−Gr
Assumptions
  • Ideal free space; isotropic reference for FSPL.
  • c = 299792458 m/s.
  • Friis free-space equation assumes far-field propagation. For electrically large antennas or short separations, verify that the antenna separation exceeds the applicable far-field distance.
Units
  • m, Hz, dBi → dB
Boundary conditions
  • Missing/≤0 d_m or f_Hz → MISSING_REQUIRED_INPUT / VALUE_MUST_BE_POSITIVE
  • Non-finite → INVALID_NUMBER
Example
d=1000 m, f=2.4 GHz → FSPL≈100.05 dB
Validation cases

4 published on this page · 10/10 tests · Production surface contract 4/4 · View evidence

  • d_m=1000, f_Hz=2.4e9 → fspl_dB≈100.052
  • same + Gt=Gr=6 → path_loss = fspl − 12
  • d_m=0 → error VALUE_MUST_BE_POSITIVE
  • missing f_Hz → error MISSING_REQUIRED_INPUT
Sources
  • Friis transmission equation — Free-space path loss form
    Supports: FSPL from distance and wavelength/frequency
  • ITU-R P.525-5 (11/2024), Calculation of free-space attenuation — Free-space basic transmission loss
    Supports: Standard FSPL formulation for radio links; version-locked recommendation
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute free-space path loss (FSPL) from distance and frequency, with optional antenna gains for a simple link budget.

Default example: 1 km · 2.4 GHz → ≈ 100.05 dB.

Supported and not supported

Supported

  • Friis FSPL in dB from d_m and f_Hz
  • Optional Gt/Gr (dBi) → antenna-adjusted link loss (path_loss_dB)
  • Wavelength λ = c/f
  • API via electrical.rf.fspl

Not supported

  • Atmospheric absorption, rain fade, or terrain models
  • Fresnel zone clearance or multipath
  • Automatic far-field / Fraunhofer check (optional antenna dimension D is not an input)
  • Full link-budget SNR / fade-margin workflows — see RF Link Budget

Agent / API notes

Capability id: electrical.rf.fspl · tool id: fspl · alias free-space-path-loss · pin calculation_version: 1.0.0.

Stable error codes: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE.

Other calculators in this family: Antenna Length Calculator, Cascaded Noise Figure Calculator, Coax Impedance Calculator, dBm to Watts Calculator, L-section LC Match Calculator, Receiver Sensitivity Calculator, Reflection Coefficient to Impedance Calculator, RF Link Budget Calculator . Explore all RF & Microwave.

→ Antenna Length Calculator Compute dipole (λ/2) or monopole (λ/4) antenna length from frequency and an empirical length factor. Runs locally in your browser. › → Cascaded Noise Figure Calculator Compute cascaded noise figure and total gain for a multi-stage RF chain using the Friis formula. Add, remove, or reorder stages. Runs locally in your browser. › → Coax Impedance Calculator Compute coaxial characteristic impedance Z0 from shield inner diameter D, center-conductor diameter d, and dielectric εr. Ideal TEM, μr≈1. Runs locally in your browser. › → dBm to Watts Calculator Convert dBm ↔ watts and dBm ↔ milliwatts with hard validation. Canonical Unit Engine for RF power. › → L-section LC Match Calculator Narrowband real RL→Z0 L-section match with dual LP/HP solutions. Runs locally in your browser. › → Receiver Sensitivity Calculator Estimate MDS: S = −174 + NF + 10·log10(BW) + SNR_min (dBm). Runs locally in your browser. › → Reflection Coefficient to Impedance Calculator Convert complex Γ ↔ normalized z (Cartesian or polar Γ). Reports VSWR and return loss. Runs locally in your browser. › → RF Link Budget Calculator Compute RF link budget: FSPL, path loss with antenna gains and misc loss, received power, and optional margin above sensitivity. Extends Free-Space Path Loss. ›
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Frequently asked questions

Key distinctions behind the calculation.

What is free-space path loss?

It is the geometric spreading loss of a radio wave between isotropic antennas in vacuum/air with no obstacles, from the Friis transmission equation. ITU-R P.525-5 calls this free-space basic transmission loss.

Is antenna-adjusted link loss the same as path loss?

No. FSPL is the isotropic-reference free-space loss. Antenna gains are separate link-budget items. The API field path_loss_dB is FSPL − Gt − Gr (antenna-adjusted link loss), not a claim that propagation loss itself changed.

Why is my measured loss higher?

Real links add cable loss, antenna inefficiency, fading, and obstruction. FSPL is an ideal free-space reference/baseline, not a guaranteed lower bound for every real propagation environment. Friis also assumes far-field conditions.

What units does the API use?

Distance in metres (d_m) and frequency in hertz (f_Hz). Gains are dBi. Display unit controls on the page do not override SI when d_m and f_Hz are present.

What if distance is zero or missing?

The API rejects with MISSING_REQUIRED_INPUT or VALUE_MUST_BE_POSITIVE.

Does CVP VERIFIED mean this live page was browser-tested?

CVP verifies the engine, REST, MCP, and SSR HTML. Live browser hydration is a separate contract (npm run test:fspl-live-e2e). Catalog tier expert_verified is internal CalculatorX domain review, not a named independent RF expert.