📡 Free Space Path Loss Calculator
Calculate signal attenuation in free space
Example: 2.4 GHz = 2.4 × 10⁹ Hz, 5 GHz = 5 × 10⁹ Hz
Line-of-sight distance between transmitter and receiver
How to Use This Calculator
Enter Frequency
Input the frequency of the radio wave in Hertz (Hz). For common frequencies: WiFi 2.4 GHz = 2.4×10⁹ Hz, WiFi 5 GHz = 5×10⁹ Hz, cellular 900 MHz = 9×10⁸ Hz. Use scientific notation for large values.
Enter Distance
Input the line-of-sight distance between the transmitter and receiver in meters. This is the straight-line distance through free space, assuming no obstacles or reflections.
Calculate
Click the "Calculate Path Loss" button to get the free space path loss in decibels (dB) and as a linear ratio. This represents the signal attenuation due to distance and frequency in ideal free space conditions.
Formula
FSPL = (4πdf/c)²
In decibels: FSPLdB = 20×log₁₀(4πdf/c)
Where:
- FSPL = Free Space Path Loss (dimensionless ratio or dB)
- d = Distance (meters, m)
- f = Frequency (Hertz, Hz)
- c = Speed of Light = 3 × 10⁸ m/s
- λ = Wavelength = c/f
Alternative Formula (d in km, f in MHz):
FSPLdB = 32.44 + 20×log₁₀(d) + 20×log₁₀(f)
Example Calculation:
For 2.4 GHz WiFi at 1 km distance:
f = 2.4 × 10⁹ Hz, d = 1000 m
FSPLdB = 32.44 + 20×log₁₀(1) + 20×log₁₀(2400)
FSPLdB = 32.44 + 0 + 67.6 = 100.04 dB
Note: Higher frequency and longer distance result in greater path loss. Path loss increases by 6 dB when distance doubles, and by 6 dB when frequency doubles.
About Free Space Path Loss Calculator
The Free Space Path Loss Calculator determines the signal attenuation that occurs when radio waves propagate through free space (vacuum or air with no obstacles). This is the fundamental loss that would occur even in ideal conditions, representing how signal power decreases with distance and frequency due to the spreading of the electromagnetic wave front.
When to Use This Calculator
- Wireless Communication: Estimate signal loss for WiFi, cellular, satellite, and radio links
- Link Budget Analysis: Calculate required transmitter power for communication systems
- Antenna Design: Understand signal propagation in free space conditions
- Satellite Communication: Calculate path loss for ground-to-satellite links
- RF Engineering: Analyze radio frequency signal propagation and link planning
Why Use Our Calculator?
- ✅ Quick Calculation: Instantly determine path loss for any frequency and distance
- ✅ Dual Units: Results in both dB (decibels) and linear ratio
- ✅ RF Applications: Essential for wireless communication system design
- ✅ Free Tool: No registration or payment required
- ✅ Educational: Learn about radio wave propagation and signal attenuation
Common Applications
WiFi and Wireless Networks: Calculate expected signal strength at different distances from access points, helping network engineers plan coverage areas and determine optimal access point placement. Higher frequencies (like 5 GHz) have more path loss than lower frequencies (2.4 GHz) at the same distance.
Satellite Communication: Estimate path loss for satellite-to-ground links, where distances are very large (hundreds to thousands of kilometers). The large path loss requires high-gain antennas and powerful transmitters for reliable communication.
Link Budget Design: Use path loss as part of a complete link budget calculation to determine if a communication link is feasible, accounting for transmitter power, antenna gains, path loss, and receiver sensitivity to ensure adequate signal-to-noise ratio.
Tips for Best Results
- Path loss increases 6 dB when distance doubles (inverse square law)
- Path loss increases 6 dB when frequency doubles (shorter wavelength)
- This is ideal free space loss - real-world losses are higher due to obstacles, atmospheric absorption, and multipath
- For terrestrial links, add 20-30 dB extra loss margin for real-world conditions
- Use link budget: Received Power = Transmitted Power + Gains - Losses
Frequently Asked Questions
What is free space path loss?
Free space path loss (FSPL) is the signal attenuation that occurs as radio waves spread out through space, even in ideal conditions with no obstacles. It's due to the inverse-square law - as distance increases, the same power is spread over a larger area, so power density decreases.
Why does path loss increase with frequency?
Path loss is proportional to (distance/λ)², where λ is wavelength. Since wavelength λ = c/f decreases as frequency increases, the path loss increases. Higher frequencies have shorter wavelengths, so they experience more path loss for the same distance.
How does path loss relate to received signal strength?
Received power Pr = Pt + Gt + Gr - FSPL (in dB), where Pt is transmitted power, Gt and Gr are antenna gains. Path loss directly reduces received signal strength.
Is this realistic for real-world conditions?
Free space path loss is the minimum loss in ideal conditions. Real-world losses are higher due to obstacles, atmospheric absorption, ground reflections, and multipath fading. For terrestrial links, add 20-40 dB margin to account for these additional losses.
Why 6 dB per doubling of distance or frequency?
Path loss ∝ (distance)², so doubling distance increases loss by 2² = 4× = 6 dB. Similarly, loss ∝ f², so doubling frequency also increases loss by 6 dB. This comes from the 20×log₁₀(2) = 6.02 dB ≈ 6 dB relationship.
Can I use this for optical communications?
Yes! The same formula applies to light waves and other electromagnetic radiation. For visible light (f ~ 5×10¹⁴ Hz), path loss is enormous even over short distances, which is why optical communications use fibers or very short line-of-sight paths.