Bell Curve Generator & Normal Distribution Plotter
Plot normal curves, shade any area, compare distributions and export a high-resolution graph for reports and slides.
Practical guides, verified formulas and interactive tools for civil engineering, hydrology, statistics and AI, built for students and working engineers.
The calculators engineers and students open most, each with plots and step-by-step working.
Plot normal curves, shade any area, compare distributions and export a high-resolution graph for reports and slides.
Convert raw scores to z-scores and percentiles with a shaded bell curve and step-by-step working.
Find the x value for any probability: left tail, right tail, central or two-tailed areas.
Area and mass moment of inertia, centroid and section properties for common and built-up shapes.
Beam bending stress from moment, section modulus and geometry, with the stress distribution plotted.
Volume of concrete for slabs, columns, beams and footings with wastage allowance.
Theory explained from first principles, with worked examples you can check.
The Laplacian filter finds edges, spots and fine detail by measuring the curvature of brightness. This guide starts from the derivative of a 1-D signal, derives the familiar 3 × 3 kernels from Taylor series, explains what the sign and the zero crossings mean, shows why the filter amplifies noise and how the Laplacian of Gaussian fixes it, and ends with blob detection, sharpening and the Laplacian in physics. Four live demos let you test each idea.
The Gaussian filter is the most widely used smoothing filter in image processing, remote sensing and computer vision. This guide builds it from nothing: what filtering is, how convolution works, where the bell curve comes from, how to compute a kernel by hand, why the filter is separable, what it does to frequencies and noise, and how to choose σ. Every idea comes with a worked example or a live demo
Four equations describe every classical electric and magnetic phenomenon, from a compass needle to Wi-Fi to sunlight. This guide states each law in integral and differential form, explains what it means physically with an example,
Every power station, transformer, electric guitar pickup and wireless charger works because a changing magnetic flux induces a voltage. This guide explains magnetic flux, Faraday's law, the direction rule of Lenz's law, motional EMF, the AC generator, transformers, inductance and eddy currents, with worked examples and an animated generator you can control.
Infiltration decides how much rain becomes runoff. This guide explains the three classic infiltration models, gives the Rawls Green-Ampt parameters for all 11 soil textures, shows how to compute ponding time, and works through the φ-index and W-index.
The FAO-56 Penman-Monteith equation is the international standard for reference evapotranspiration. This guide explains every term, walks through all twelve calculation steps, reproduces the official FAO worked example (ET₀ = 3.9 mm/day),
The Gaussian filter is the most widely used smoothing filter in image processing, remote sensing and computer vision. This guide builds it from nothing: what filtering is, how convolution works, where the bell curve comes from, how to compute a kernel by hand, why the filter is separable, what it does to frequencies and noise, and how to choose σ. Every idea comes with a worked example or a live demo
Apply the 4-neighbour, 8-neighbour or isotropic Laplacian kernel, the Laplacian of Gaussian or a Difference of Gaussians to a test image or your own photo. View the signed response, find edges as zero crossings, sharpen the image, and see why smoothing must come before the second derivative. Click any pixel to see the arithmetic.
Generate a normalized Gaussian kernel for any sigma, see exactly how its weights are computed, and apply it to a test image or your own photo. Add noise, measure the improvement in PSNR, find the best sigma, and compare the filter's frequency response with a box filter. Every calculation runs in your browser.
Compute the magnetic flux density B produced by steady currents in the six most common conductor shapes, using the Biot–Savart law and Ampère's law. The calculator gives B in tesla, millitesla, microtesla and gauss, plots the field along the axis, maps the exact off-axis field of a loop, compares finite and ideal solenoids, and shows the substituted formula for every result.
Place up to eight point charges, drag them around, and watch the electric field lines and equipotential lines update live. Move the probe to read the electric field vector and potential at any point, see the net Coulomb force on every charge, or use the quick Coulomb's law calculator for two charges in any medium.
Paste a monthly rainfall series and get the SPI at 1 to 24 months using the standard McKee et al. (1993) gamma method, the drought category of every month, a list of drought events with duration and severity, and a multi-scale heatmap that shows how short dry spells grow into long droughts.
Methods follow standard textbooks and codes, cited on each page, and worked examples are checked independently.
See every intermediate value, not just the answer, so you can learn the method and check your own work.
Plots update as you type. Export graphs and results for assignments, reports and presentations.
No account, no paywall, no install. Every tool works in the browser on phones, tablets and desktops.
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Students, civil engineering graduates, and working professionals who want practical knowledge, especially those integrating AI, ML, and Python into their engineering practice.
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