Amplitude-to-Intensity Calculator: Fast Conversion Tool for Signal Analysis

Amplitude-to-Intensity Calculator: Formula, Units, and Common Applications

For fields where intensity I is proportional to the square of the amplitude A (common in waves, optics, acoustics):
- I = k · A^2
- Often k = 1 when amplitude and intensity use consistent units or when reporting relative intensity: I ∝ A^2.
For time-varying signals, use mean-square value (for RMS amplitude Arms):
- I (or power-related quantity) ∝ Arms^2, where Arms = sqrt( (1/T) ∫_0^T [A(t)]^2 dt ).
For complex-valued amplitudes (phasors) E:
- I ∝ |E|^2 = E · E*, where Eis the complex conjugate.

Amplitude units depend on the physical quantity:
- Optics (electric field): amplitude in V/m → intensity in W/m^2 after including impedance/factor.
- Acoustics (pressure): amplitude in Pa → acoustic intensity in W/m^2 requires medium properties (e.g., density, sound speed).
- Electrical signals (voltage/current): amplitude in V or A → power in W depends on load impedance R: P = V_rms^2 / R.
When using I = A^2 with no additional constants, results are in arbitrary or relative units (useful for normalized comparisons).
Always include medium- or system-specific constants (e.g., 1/(2Z0) for plane EM waves in free space) to convert to absolute intensity/power units.

Optics and photonics: converting electric-field amplitude to optical irradiance (W/m^2) for lasers, detectors, and imaging.
Acoustics: converting pressure amplitude to acoustic intensity or sound power for noise analysis and speaker design.
Radio-frequency and microwave engineering: converting voltage/current amplitude at a known impedance to delivered power.
Signal processing: computing power or energy of time signals from amplitude samples (using RMS or mean-square).
Experimental calibration and measurement: comparing relative intensities, detector responsivity, and system linearity.

Use RMS or mean-square for time-varying signals; peak amplitude squared gives peak intensity, not average.
Account for impedance, medium properties, and geometry to convert from proportional intensity to absolute units.
For logarithmic measures (dB): level (dB) = 10·log10(I/I0) if using intensity/power, or 20·log10(A/A0) when starting from amplitude.