Distance Attenuation Calculator
Calculate power loss due to distance (inverse square law)
How to Use This Calculator
Enter Initial Power
Input the power at the source (P₀) in Watts. This is the power at distance zero.
Enter Distance
Input the distance from the source (d) in meters. The power decreases with distance squared.
Calculate
Click calculate to get the final power and attenuation using the inverse square law.
Formula
P = P₀ / d²
where P = final power (W), P₀ = initial power (W), d = distance (m)
Attenuation (dB) = 10 × log₁₀(P₀ / P)
Example:
If initial power is 100 W at distance 10 m:
P = 100 / (10²) = 100 / 100 = 1 W
Attenuation = 10 × log₁₀(100 / 1) = 10 × 2 = 20 dB
The power decreases by a factor of 100 (20 dB) when distance increases by 10×.
About Distance Attenuation Calculator
The Distance Attenuation Calculator determines how power decreases with distance using the inverse square law. This law applies to point sources that radiate energy uniformly in all directions, such as sound sources, radio transmitters, and light sources.
When to Use This Calculator
- Acoustics: Calculate sound power loss with distance
- RF Engineering: Determine signal strength at different distances
- Lighting Design: Calculate illumination levels at various distances
- Radio Communications: Estimate signal range and coverage
- Audio Systems: Design speaker placement and coverage
- Physics Education: Understand inverse square law principles
Why Use Our Calculator?
- ✅ Quick Calculations: Get power loss instantly
- ✅ Accurate Results: Uses inverse square law formula
- ✅ Attenuation in dB: Provides both power and decibel values
- ✅ Educational: Learn about inverse square law
- ✅ Free Tool: No registration required
Understanding Inverse Square Law
The inverse square law states that power decreases proportionally to the square of the distance. When you double the distance, power decreases by a factor of 4 (6 dB). When you triple the distance, power decreases by a factor of 9 (9.5 dB).
- Power is inversely proportional to distance squared
- Doubling distance = 4× power decrease (6 dB loss)
- Tripling distance = 9× power decrease (9.5 dB loss)
- Only applies to point sources in free space
- Real-world factors (reflections, absorption) may modify this
Practical Applications
- Sound Systems: Calculate speaker coverage and power requirements
- Radio Links: Estimate signal strength for wireless communications
- Lighting: Determine illumination levels for lighting design
- Radar: Calculate detection range based on transmitter power
Frequently Asked Questions
What is the inverse square law?
The inverse square law states that power decreases proportionally to the square of distance from a point source: P = P₀/d². This applies to sound, light, radio waves, and other forms of radiation.
Why does power decrease with distance squared?
As energy radiates from a point source, it spreads over an increasing area. The area of a sphere increases with r², so power per unit area (intensity) decreases as 1/r².
Does this apply to all sound sources?
The inverse square law applies to point sources in free space. For directional sources, line sources, or sources near boundaries, the attenuation may differ from the inverse square law.
How much does power decrease when distance doubles?
When distance doubles, power decreases by a factor of 4 (d² = 2² = 4). This corresponds to a 6 dB attenuation (10 × log₁₀(4) ≈ 6).
What factors affect real-world attenuation?
Real-world attenuation may be affected by absorption, reflections, atmospheric conditions, obstacles, and the directional characteristics of the source, which can modify the simple inverse square law.