Analyze Gaussian pulse width, envelope, energy, and carrier behavior. Enter values, compare width modes, and export clean results instantly.
| Case | Peak Amplitude | Time | Center | Width Mode | Width Value | Carrier Frequency | Phase |
|---|---|---|---|---|---|---|---|
| Pulse A | 5.0 | 2.0 | 0.0 | Sigma | 3.0 | 0.25 | 0.0 |
| Pulse B | 8.0 | 1.5 | 0.5 | Intensity FWHM | 2.4 | 0.5 | 0.7854 |
| Pulse C | 12.0 | -1.0 | 0.0 | Amplitude FWHM | 4.2 | 0.1 | 1.5708 |
The Gaussian pulse envelope is:
A(t) = A0 × exp( - (t - t0)2 / (2σ2) )
The normalized envelope is:
exp( - (t - t0)2 / (2σ2) )
The intensity ratio is:
I(t) / I0 = exp( - (t - t0)2 / σ2 )
The carrier modulated field is:
E(t) = A(t) × cos(2πft + φ)
Width conversions used in the calculator:
A Gaussian pulse is a smooth waveform with maximum value at its center. Its amplitude falls symmetrically on both sides. This shape appears in optics, signal processing, laser physics, ultrafast measurements, and communication analysis. Engineers and students use it because the math is clean and the physical behavior is realistic.
Pulse width can be described in several ways. Some users work with sigma. Others use amplitude FWHM, intensity FWHM, or the one over e squared intensity radius. These terms are related, but they are not equal. A practical calculator must convert them correctly before evaluating amplitude, energy, or time spread.
This Gaussian pulse calculator helps you analyze envelope amplitude, normalized envelope, intensity ratio, and carrier based field value at a selected time. It also converts width forms into sigma and reports derived width metrics. This makes the tool useful for quick checks, class exercises, lab preparation, and design review work.
When the selected time is near the center, the envelope remains high. As the time moves away from the center, the exponential term reduces the signal rapidly. Intensity decays faster than amplitude because it depends on the square of the field. This difference matters in pulse energy studies and detector response calculations.
Gaussian pulses are common in transform limited systems. For that reason, temporal width often connects to spectral width. This page provides an approximate spectral FWHM from the temporal intensity FWHM. It gives a convenient reference when you need a fast estimate for bandwidth, pulse compression, or short pulse characterization.
The calculator also supports CSV and PDF export. That is helpful for documentation, lab notes, and team review. The example table shows typical values and helps users confirm input structure. Together, these features turn a simple formula page into a practical Gaussian pulse analysis tool for repeated use.
A Gaussian pulse is a waveform whose envelope follows a Gaussian function. It peaks at the center and decays smoothly on both sides. It is widely used in optics, electronics, and signal analysis.
Different books and labs describe pulse width differently. This calculator lets you enter sigma, amplitude FWHM, intensity FWHM, or one over e squared intensity radius and converts them consistently.
Amplitude describes the field envelope. Intensity is proportional to the square of the field. Because of that, intensity usually narrows or decays differently in formulas compared with amplitude.
It shows the Gaussian envelope multiplied by the carrier cosine term. This is useful when you want the actual modulated field value instead of only the envelope magnitude.
Yes. Negative time values are valid if they match your reference system. The calculator only evaluates the pulse relative to the entered center time and width.
Use one consistent unit system. For example, if time is in seconds, then width must also be in seconds, and carrier frequency should be in cycles per second.
The reported spectral width uses a common transform limited Gaussian relation. It is a practical estimate and assumes an ideal Gaussian pulse without chirp or extra distortions.
Use CSV for spreadsheet analysis and repeated comparisons. Use PDF for reports, lab records, submissions, or sharing a fixed result snapshot with others.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.