Calculus Calculator
Solve derivatives, integrals and limits instantly, with clear step-by-step solutions. Free, accurate and built for students and engineers.
Built for accuracy
Auto-format
The parser detects implied multiplication, so 2x or xsin(x) are read correctly as 2*x and x*sin(x).
All in one
Differentiation (chain and product rule), definite and indefinite integration, and limits (including at infinity) in a single interface.
Clean answers
Exact algebraic results like cos(x) + 2x instead of rough decimals. Ideal for engineering mathematics.
What is a calculus calculator?
A calculus calculator is an online math tool that helps students, engineers and researchers solve complex problems without working every step by hand. This free calculator computes derivatives, integrals (definite and indefinite) and limits of functions involving variables, trigonometric expressions, exponentials and logarithms.
Whether you are preparing for a university exam, checking homework, or working through engineering problems, it gives accurate step-by-step solutions in seconds using a powerful symbolic math engine, so you get clean algebraic answers instead of messy decimal approximations.
How to use this calculus calculator
- Choose your operation: select Differentiate, Integrate or Find limit.
- Enter your function: use the on-screen keypad or type directly, e.g.
x^2 * sin(x). - Set parameters: for integrals pick definite or indefinite; for limits enter the value x approaches and the direction.
- Compute: the result appears instantly with step-by-step reasoning.
Derivative calculator, how differentiation works
The derivative measures how quickly a function changes with respect to its input. This calculator applies the core rules:
- Power rule: d/dx[xⁿ] = n·xⁿ⁻¹, so the derivative of x³ is 3x².
- Product rule: d/dx[f·g] = f'g + fg', for two functions multiplied together.
- Quotient rule: d/dx[f/g] = (f'g − fg') / g².
- Chain rule: d/dx[f(g(x))] = f'(g(x))·g'(x), for composite functions like sin(x²).
- Trig, exp and log: d/dx[sin x] = cos x, d/dx[eˣ] = eˣ, d/dx[ln x] = 1/x.
Integral calculator, definite and indefinite
Integration is the reverse of differentiation and is used to find areas, volumes and antiderivatives. This tool handles both types:
- Indefinite integrals: the antiderivative plus a constant, e.g. ∫x² dx = x³/3 + C.
- Definite integrals: the net area under a curve between two bounds a and b.
Limit calculator, step by step
Limits describe the value a function approaches as the input gets closer to a point. This calculator handles limits at finite points, limits at infinity, one-sided limits, and common indeterminate forms like 0/0 or ∞/∞.