Coordinate geometry
LiveDistance Between Two Points
Measure the shortest route between two coordinates, with the right-triangle behind the formula drawn beside the answer.
Engineering maths tools
Engineering maths you can test, not just read.
Work through coordinates, complex numbers, vectors, equations, matrices, differentiation, and approximation with calculators that keep the algebra visible. Change the inputs, read the substitution, then use the diagram to check whether the answer makes sense.
Formula shown
Substitution shown
Edge cases flagged
Quick check
Distance preview
A(1, 2)
B(6, 5)
d = sqrt(34) = 5.831
Live tools
Start where the problem starts
Each page is built around a real calculation, then supported with the small bit of explanation that makes the formula easier to check by eye.
Coordinate geometry
LiveGradient of a Line
Turn two points into a slope and see the rise-run triangle that controls the steepness of the line.
Coordinate geometry
LiveLine Through Two Points
Build the equation of the unique straight line through two points, including vertical-line cases.
Coordinate geometry
LivePoint-to-Line Distance
Find the perpendicular gap from a point to a line in general form, with the scaling of the normal made explicit.
Complex numbers
LiveArgand Diagram Plotter
Place a complex number on the real-imaginary plane and read its modulus and angle from the picture.
Complex numbers
LiveComplex Polar Converter
Convert a + bi into modulus-argument form without losing the quadrant information.
Complex numbers
LiveComplex Number Calculator
Work through complex arithmetic while keeping rectangular and polar meaning visible.
Complex numbers
LiveRoots of Unity Visualiser
See the nth roots of unity as equally spaced points around the unit circle.
Vector algebra
Live2D Vector Calculator
Add or subtract 2D vectors and read the resultant as both components and a direction.
Vector algebra
LiveDot Product Calculator
Calculate a scalar product and connect it to angle, projection, and work done.
Vector algebra
LiveAngle Between Vectors
Find the angle between two vectors using the dot product ratio, with zero-vector checks included.
Vector algebra
LiveCross Product Calculator
Calculate A x B, its magnitude, and the area it represents.
Vector algebra
LiveArea From Cross Product
Use the cross product magnitude to get parallelogram and triangle area from side vectors.
Engineering applications
LiveAC Impedance Calculator
Calculate series RLC impedance and see resistance and reactance as a complex number.
Engineering applications
LiveWork Done Vector Calculator
Find work done from force and displacement using the dot product.
Engineering applications
LiveTorque / Moment Calculator
Calculate the moment of a force as r x F and read its turning effect.
Linear systems
Live2x2 Linear System Solver
Solve two linear equations and see whether the lines meet once, never meet, or are really the same line.
Linear systems
LiveGaussian Elimination Solver
Solve a 3x3 system by row reduction, with each elimination step kept in view.
Matrix methods
LiveMatrix Row Operations Visualiser
Try a single row operation and see exactly which entries change.
Linear systems
LiveBack Substitution Calculator
Start from an upper triangular system and solve it from the bottom upward.
Solution checks
LiveLinear System Residual Checker
Test a proposed solution by calculating Ax - b and measuring the leftover error.
Numerical stability
LivePivoting Explainer
Pick the best pivot row by comparing absolute values in the active column.
Circuit systems
LiveKirchhoff Linear System Example
Solve loop-current style equations as a matrix system A i = v.
Differentiation rules
LiveDerivative Rule Explorer
Search the core derivative rules and see the warning that goes with each one.
Rates of change
LiveCrank-Piston Differentiation Simulator
Turn crank geometry into displacement, velocity, and acceleration values.
Taylor and approximation
LiveTaylor Series Centre Explorer
Build a Taylor polynomial around a chosen centre and compare it with the true function.
Numerical differentiation
LiveCentral Difference Derivative Lab
Estimate first and second derivatives from values on both sides of a point.
Limits and errors
LiveL'Hopital Limit Checker
Check a quotient limit before applying L'Hopital's rule.
Limits and errors
LiveError Propagation Calculator
Estimate how measurement uncertainty affects a calculated quantity.
Optimisation
LiveHigher-Derivative Stationary Point Classifier
Classify a stationary point when the second derivative test gives zero.
Optimisation
LiveOne-Dimensional Optimisation Search Simulator
Sample an interval, check endpoints, and keep the best value found.