Starlight Tools

Starlight Tools directory

Calculus Calculators

19 free, browser-based tools. No account required.

Evaluate limits, differentiate functions and equations, solve first-order initial-value problems, test infinite series, construct Taylor and Maclaurin polynomials, and calculate proper or improper integrals, Riemann sums, curve lengths, volumes, and surface areas of revolution while inspecting the rules used and connecting results to graphs with private browser-based calculus tools. Start with the Differential Equation Calculator, Limit Calculator, Derivative Calculator with Steps, Series Convergence Calculator, Integral Calculator with Steps, Volume of Revolution Calculator, Surface Area of Revolution Calculator, or Arc Length Calculator.

Yellow star mascot drawing a solution curve through a differential equation slope field

Differential Equation Calculator for First-Order ODEs

Solve first-order initial-value problems numerically with RK4, improved Euler, or Euler methods, step-doubling estimates, graphs, tables, and CSV export. v1.0

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Yellow star mascot rotating a curve into a hollow surface of revolution

Surface Area of Revolution Calculator for Functions and Curves

Calculate curved surface area for explicit or parametric curves rotated around horizontal or vertical lines, with shifted axes, derivatives, setup graphs, validation, and CSV data. v1.0

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Yellow star mascot showing disks and washers inside a volume of revolution

Volume of Revolution Calculator with Disk, Washer and Shell Methods

Calculate solids of revolution about horizontal or vertical lines with disk, washer, and cylindrical shell integrals, region graphs, validation, and CSV data. v1.0

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Yellow star mascot measuring the arc length of a curved graph

Arc Length Calculator for Functions and Parametric Curves

Calculate curve length for y=f(x) or x(t), y(t) with symbolic derivatives, adaptive numerical integration, graphs, copied summaries, and CSV samples. v1.0

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Yellow star mascot timing the changing radius of an expanding circle

Related Rates Calculator with Steps

Solve circle, sphere, ladder, tank, perpendicular-motion, and rectangle related-rates models with signed rates, consistent units, and step-by-step differentiation. v1.0

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Yellow star mascot comparing maximum and minimum points on a curve

Calculus Optimization Calculator for Maximum and Minimum Values

Find local and absolute extrema on a closed interval using derivatives, critical points, endpoint comparison, classification, graphs, and downloadable results. v1.0

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Yellow star mascot examining shrinking series terms approaching infinity

Series Convergence Calculator with Tests and Steps

Classify infinite series as absolutely convergent, conditionally convergent, divergent, or inconclusive using transparent tests, partial sums, graphs, and downloadable steps. v1.0

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Yellow star mascot checking an improper integral near a singularity and infinity

Improper Integral Convergence Calculator

Test infinite bounds and isolated singularities one side at a time, with exact antiderivative limits, absolute-convergence checks, cutoff evidence, graphs, and CSV export. v1.0

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Yellow star mascot building Taylor-series approximations around an expansion point

Taylor and Maclaurin Series Calculator with Steps

Build Taylor polynomials about any center or Maclaurin polynomials at zero through order 10, with derivative coefficients, point errors, graphs, copying, and text export. v1.0

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Yellow star mascot arranging Riemann-sum rectangles beneath a curve

Riemann Sum Calculator

Calculate and compare left-endpoint, right-endpoint, and midpoint Riemann sums with sample points, numerical reference values, rectangle graphs, and CSV export. v1.0

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Yellow star mascot showing tangent and normal lines at a point on a curve

Tangent and Normal Line Calculator

Find the point, derivative, tangent slope, perpendicular normal slope, line equations, construction steps, and graph for y=f(x). v1.0

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Yellow star mascot drawing a tangent on an implicit curve

Implicit Differentiation Calculator with Steps

Find exact first implicit derivatives from equations, inspect both partial derivatives and calculus rules, and check slopes, vertical tangents, or singular points. v1.0

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Yellow star mascot showing a directional slice through a multivariable surface

Partial Derivative Calculator with Steps

Calculate first, higher-order, and mixed partial derivatives with exact symbolic results, rule-by-rule steps, point evaluation, and downloadable working. v1.0

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Yellow star mascot comparing gradient and direction arrows on a contour map

Directional Derivative and Gradient Calculator

Find a symbolic gradient, evaluate it at a point, normalize any nonzero direction vector, and calculate the directional derivative with dot-product steps. v1.0

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Yellow star mascot presenting a Jacobian matrix and transformed coordinate grid

Jacobian Matrix Calculator with Steps

Build symbolic Jacobian matrices for up to six functions and variables, evaluate them at a point, and inspect every partial derivative step. v1.0

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Yellow star mascot examining a Hessian matrix and classified critical points

Hessian Matrix and Critical Point Calculator

Build symbolic Hessian matrices, search bounded regions for critical points, and classify local minima, maxima, saddle points, and degenerate cases. v1.0

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Yellow star mascot presenting a derivative graph and tangent line

Derivative Calculator with Steps

Differentiate common functions using product, quotient, chain, power, trigonometric, exponential, and logarithmic rules. Includes higher derivatives, point values, steps, and graphs. v1.0

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Yellow star mascot presenting an integral and shaded area under a graph

Integral Calculator with Steps

Find verified antiderivatives or calculate finite definite integrals with symbolic rules, adaptive numerical fallback, bounds evaluation, steps, and signed-area graphs. v1.0

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Yellow star mascot presenting two curves approaching an open limit point

Limit Calculator with Steps

Evaluate two-sided, one-sided, and infinite limits using direct substitution, repeated L’Hôpital’s rule, leading-term analysis, numerical checks, DNE detection, steps, and graphs. v1.0

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About These Calculus Calculators

These tools are designed to make calculus operations transparent by pairing exact symbolic results with the rules, intermediate expressions, numerical checks, and visualizations used to obtain them. Calculations run locally in your browser.