Practical, free calculators for structural, geotechnical, hydraulic, statistical and survey problems. Results update instantly with charts and step-by-step working.
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.
Paste annual maximum floods and get the 2- to 1000-year design floods from four distributions side by side, Gumbel confidence limits, a Gumbel probability plot with your data, a goodness-of-fit ranking, the return period of any given flood, and the full step-by-step
Estimate direct runoff depth and volume from a storm with the SCS-CN (NRCS curve number) method. Build a composite curve number from the complete TR-55 tables,
Paste a time series and get the Mann-Kendall S statistic, variance (with tie correction), Z, p-value, Kendall's τ and Sen's slope with its confidence interval. Includes the Hamed-Rao and trend-free pre-whitening corrections for autocorrelated data,
Compute asphalt tonnage, volume, quantity and total project cost for any paving job. Covers driveways, parking lots, roads and footpaths. Supports hot mix asphalt, cold mix, dense-graded, SMA and millings with accurate 2026 pricing data.
This Tool Generates a complete Gale's traverse table from bearings and distances. Calculates latitudes, departures, closing errors, Bowditch (compass rule) and Transit corrections, adjusted coordinates, adjusted bearings and lengths. Includes full step-by-step workings.
Calculate area moment of inertia (second moment of area) and mass moment of inertia for all standard shapes. Live annotated diagrams update as you type. Full step-by-step solutions, parallel axis theorem, and all unit systems.
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,
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