Free Space Path Loss
FSPL = 20log(d) + 20log(f) + const
Quick answer
This calculator solves FSPL(dB) = 20log₁₀(d) + 20log₁₀(f) + 20log₁₀(4π/c) for FSPL. With Distance 1 m, Frequency 2.4 GHz, the result is 40.05 dB.
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Formula
Description
Free space path loss (FSPL) quantifies the attenuation of a radio signal propagating through free space with no obstacles. It increases with both distance and frequency: doubling the distance adds 6 dB of loss, and doubling the frequency also adds 6 dB. This is not because higher frequencies are more attenuated, but because a fixed-size receiving antenna captures a smaller fraction of the expanding wavefront at shorter wavelengths. FSPL is the baseline loss used in link budget calculations; real-world losses from obstacles, reflections, and atmospheric absorption are additional.
Variables
- FSPL — Path loss in decibels (dB)
- d — Distance between transmitter and receiver (m)
- f — Signal frequency (Hz)
- c — Speed of light ≈ 3 × 10⁸ m/s
Practical Notes
At 2.4 GHz, FSPL at 1m is about 40 dB, at 10m about 60 dB, and at 100m about 80 dB. Indoor environments add 10-30 dB of additional loss from walls and objects. For 5 GHz WiFi, add about 6 dB more loss compared to 2.4 GHz at the same distance.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| d | Distance | m | mm, cm, m, km |
| f | Frequency | GHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Distance 1 m, Frequency 2.4 GHz
- 2. The relation: FSPL(dB) = 20log₁₀(d) + 20log₁₀(f) + 20log₁₀(4π/c)
- 3. Substitute: d = 1 m, f = 2.4 GHz
- 4. Result: FSPL = 40.05 dB
Worked examples
Minimum range
Given: Distance 1 mm, Frequency 100 MHz
Result: FSPL = -47.55 dB
Low range
Given: Distance 10 mm, Frequency 1 GHz
Result: FSPL = -7.552 dB
Typical
Given: Distance 1 m, Frequency 2.4 GHz
Result: FSPL = 40.05 dB
High range
Given: Distance 100 m, Frequency 10 GHz
Result: FSPL = 92.45 dB
Maximum range
Given: Distance 1 km, Frequency 100 GHz
Result: FSPL = 132.4 dB
How FSPL changes with Distance
| Distance (input) | FSPL (result) |
|---|---|
| 10 cm | 20.05 dB |
| 25 cm | 28.01 dB |
| 50 cm | 34.03 dB |
| 0.75 m | 37.55 dB |
| 1 m | 40.05 dB |
| 1.5 m | 43.57 dB |
| 2 m | 46.07 dB |
| 4 m | 52.09 dB |
| 7 m | 56.95 dB |
| 10 m | 60.05 dB |
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<p><a href="https://vbatpower.com/formulas/free-space-path-loss/">Free Space Path Loss</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Free Space Path Loss?
Use FSPL(dB) = 20log₁₀(d) + 20log₁₀(f) + 20log₁₀(4π/c). With Distance 1 m, Frequency 2.4 GHz, FSPL works out to 40.05 dB.
What is the formula for Free Space Path Loss?
The formula is FSPL(dB) = 20log₁₀(d) + 20log₁₀(f) + 20log₁₀(4π/c). Free space path loss (FSPL) quantifies the attenuation of a radio signal propagating through free space with no obstacles.
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