Math Tools: Formula, Calculus, Matrix, Equations & Geometry

Math Tools is a workbench of eight panels behind one tab bar. The formula library holds 96 cards, each opened as a calculator with its own inputs. The other seven panels cover calculus (derivative, integral, limit, Taylor), matrix algebra (twelve operations, from determinant to matrix exponential), equations (polynomial roots, linear systems, numeric roots), complex arithmetic, number theory, geometry and step-by-step derivations. Every panel has its own URL, so a calculation can be linked or bookmarked. Inputs stay in the browser, and results keep a working value that can be copied, stored or sent onward.

Math Tools: Formula, Calculus, Matrix, Equations & Geometry

How to run a calculation

Choose a panelfrom the tab bar — Formulas, Calculus, Matrix, Equations, Complex, Number Theory, Geometry or Step-by-step.
Type the input.Expressions use calculator syntax: x^2, x^3 + 2*x^2 - 5*x + 3, (1 - cos(x))/x^2. Matrices are entered one number per cell after setting Rows and Cols, or loaded from the workspace.
Pick the operation and press Compute(Solve in Equations). The readout appears in the Result box; an integral or limit marked ≈ carries an error estimate on the line below.
Watch the mode tabs.Calculus switches between Derivative, Integral, Limit and Taylor; Integral adds the bounds a and b, Limit the point, Taylor the order and expansion point.
Check or reuse.The Step-by-step panel shows the rule applied at each step; results that carry a value can be stored under a variable name or sent onward.

Worked examples

Every readout below was produced by the live panels; the same inputs reproduce them.

Panel · mode	Input	Readout
Calculus · Derivative	f(x) = `x^3 + 2x^2 - 5x + 3`	*3 x ^ 2 + 4 * x - 5**
Calculus · Integral	f(x) = `x^2`, a = 0, b = 1	∫ ≈ 0.3333333333, error ±3.70e-15
Calculus · Integral	f(x) = `x^2`, a = 0, b = 3	∫ ≈ 9, error ±9.99e-14
Calculus · Limit	`(1 - cos(x))/x^2`, x → 0	0.4999999994 left and right; extrapolation error ±6.94e-10
Matrix · Det	A = `6 1 1 / 4 −2 5 / 2 8 7`	-306
Matrix · Rank	the same A	3, with zero tolerance 5.33e-15
Geometry · Triangle	sides a = 3, b = 4, c = 5	area 6, perimeter 12, inradius 1, circumradius 2.5, angles 36.8699° / 53.1301° / 90°

The derivative is exact algebra — multiplied out it is 3x² + 4x − 5. The integral and limit readouts are numeric: 0.3333333333 is rounded from 1/3, and 0.4999999994 is the sampled value of a limit whose true value is 1/2, so the digits after the printed error belong to the method, not to the function.

Limits to keep in mind

Numeric answers come with error lines, so read them before quoting digits.: An integral returns a value plus an error estimate, and an integrable endpoint singularity such as 1/sqrt(x) on [0, 1] returns ∫ ≈ 2 with a note on how it was removed; a limit is checked from both sides and reported as non-existent when they disagree; a matrix at the edge of the working precision is flagged as singular or near-singular.
What it does not do: it is not a computer-algebra system.: The calculus panel returns no antiderivative formula and does not simplify expressions — for symbolic work with the rule at each step, use the Step-by-step panel. For a plotted function use the graphing calculator; for a single expression with precedence and angle modes, the scientific calculator.

The exact/numeric split

The signature trap is that the panels mix two kinds of answer under one Result label. A derivative (and every step-by-step result) is a formula: x^3 + 2*x^2 - 5*x + 3 becomes 3 * x ^ 2 + 4 * x - 5, exact under the rules it supports. An integral, limit, numeric root or eigenvalue is a computed number: ∫ ≈ 0.3333333333 on [0, 1] and 0.4999999994 for (1 - cos(x))/x^2 near 0 are correct to the stated error and no further. When an answer must be a closed form, take it from the step-by-step panel's integral tab, not the calculus panel.

Where it fits

Checking homework answers

Differentiate a polynomial and compare with the printed answer — the cubic above gives 3x² + 4x − 5 — or solve coefficients 1, -6, 11, -6 in the equations panel: the roots read 1.00000000, 2.00000000 and 3.00000000.

Geometry and measurement

Enter sides 3, 4 and 5 in the geometry triangle tab: the panel detects SSS, classifies the shape as a right scalene triangle, and returns area 6, perimeter 12, inradius 1 and circumradius 2.5, with heights 4 / 3 / 2.4. The plane, solid and coordinate tabs handle circles, cylinders, polygon areas and line intersections.

Discrete mathematics

Number theory answers "is 97 prime" with the neighbouring primes (89 and 101), factors integers, inverts a value modulo n, converts between bases 2 and 36, and demonstrates CRT and RSA round trips with exact big-integer arithmetic.

Privacy

All eight panels compute inside your browser; nothing you type or calculate is uploaded.

References

Wikipedia, Derivative, en.wikipedia.org （访问日期：2026-09-30）— definition of the derivative.
Wikipedia, Limit of a function, en.wikipedia.org （访问日期：2026-09-30）— one-sided and two-sided limits.
Wikipedia, Numerical integration, en.wikipedia.org （访问日期：2026-09-30）— quadrature and its error estimates.
Wikipedia, Determinant, en.wikipedia.org （访问日期：2026-09-30）— determinant properties and the singular case.
Wikipedia, Triangle, en.wikipedia.org （访问日期：2026-09-30）— area, inradius and circumradius relations.
NIST, Digital Library of Mathematical Functions, §1.4 Calculus of One Variable, dlmf.nist.gov （访问日期：2026-09-30）— limits and differentiation.

Sources & review

Reviewed by: CalcX Editorial Team
Updated: 2026-09-30