Shot Noise Calculator
Enter DC current and bandwidth to compute shot-noise current i_n=√(2e·I·B). I=1 mA, B=1 MHz, e=1.602e-19 → i_n≈17.9 nA (RMS). It is the Poisson granularity of charge.
Input Data
Results
At a glance:Shot noise (shot noise): the random fluctuation of an electric current caused by charge arriving in discrete quanta (electrons), a Poisson process. The RMS noise current is i_n=√(2e·I·B), where i_n is the RMS noise current (A), e=1.602176634×10⁻¹⁹ C the elementary charge, I the DC current (A) and B the measurement bandwidth (Hz). Term by term: I is the average current (the arrival rate of electrons); B is the measurement bandwidth — a wider band passes more independent fluctuation samples, and the noise grows as √B; the √2eI is the noise spectral density (A/√Hz), i.e. the noise per unit bandwidth. Physical meaning: current is not perfectly smooth; the discrete arrival of electrons produces a Poisson fluctuation whose RMS grows with √I and √B. Unlike thermal (Johnson) noise, which exists without current, shot noise requires a current (the charge flow itself is granular). Example: I=1 mA, B=1 MHz → i_n=√(2×1.602e-19×0.001×1e6)=√(3.204e-16)=1.79e-8 A=17.9 nA. The noise density √(2eI)=√(2×1.602e-19×0.001)=√(3.204e-22)=1.79e-11 A/√Hz. History: Schottky (1918) first analysed it (he called it 'Schroteffekt', shot effect), explaining the hiss in vacuum-tube currents. Applications: (1) photodiodes and avalanche detectors — the photocurrent shot noise sets the sensitivity floor; (2) radio receiver front ends — the first-stage current noise limits the signal-to-noise ratio; (3) low-current measurement and standard cells; (4) quantum-limited sensing; (5) optical communication receivers.
Formula
RMS noise: i_n = √(2·e·I·B)
Spectral density: S_I = 2·e·I (A²/Hz)
Noise density: √(2·e·I) (A/√Hz)
e = 1.602176634×10⁻¹⁹ C (exact)
$$i_n = \sqrt{2 e I B}, \quad S_I = 2 e I, \quad e = 1.602\times 10^{-19}\ \mathrm{C}$$How to Use
- Enter DC current I (A) and bandwidth B (Hz).
- The tool computes i_n=√(2eIB), the noise density √(2eI) and the charge e.
Case Studies
Photodiode receiver sensitivity
A photodiode: I=1 mA, B=1 MHz → i_n=17.9 nA (RMS).
For a 1 μA signal the S/N≈56, limiting weak-light detection.
Wider B (10 MHz) raises i_n to 56.6 nA — bandwidth must be matched to the signal to keep noise low.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.