How to run a calculation 01 Choose a panel from the tab bar — Formulas, Calculus, Matrix, Equations, Complex, Number Theory, Geometry or Step-by-step. 02 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. 03 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. 04 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. 05 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 + 2*x^2 - 5*x + 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 → 00.4999999994 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.
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Reviewed by CalcX Editorial Team
Updated 2026-09-30