ƒ MATH · EIGHT CALCULATION MODES

Numerical Calculus Calculator

Approximate a definite integral or derivative at a point for a real-valued function. Enter f(x), bounds or an evaluation point. How to use it ↓

Approximate a definite integral or derivative at a point for a real-valued function. Enter f(x), bounds or an evaluation point.

Operation f(x)

Lower boundUpper bound

Numerical approximation for real-valued functions. Trigonometric functions use the selected DEG/RAD setting.

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About this result

Results round to 12 significant digits. Exact arithmetic fractions are available where supported.

Expression reference

sin(30) · asin(0.5)
ln(e) · log(8,2)
root(27,3) · 2^3
5! · nCr(5,2)
sinh(1) · conj(3+4i)
re(3+4i) · arg(3+4i)
1e-5 · 200+10%

Use exp(x) for eˣ and mod(a,b) for the remainder. Roots and logarithms may return complex values.

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How to use the numerical calculus calculator

Choose Definite integral or Derivative at a point.
Enter a real-valued function using x, such as x^2 or sin(x).
For integration, enter lower and upper bounds. For differentiation, enter the evaluation point.
Check DEG/RAD for trigonometric functions and select Calculate. Read the numerical estimate and its method notes.

Formula and method

Definite integral: ∫ₐᵇ f(x) dx; derivative at a point: f′(x₀)

Definite integration

The integral measures signed accumulation between the bounds. Adaptive Simpson integration subdivides the interval to compare numerical estimates. Reversing the bounds changes the sign. The result is a numeric estimate, not a symbolic antiderivative.

Differentiation at a point

A derivative measures the local rate of change. This calculator compares five-point estimates at two step sizes. For a smooth function, nearby samples estimate the slope without rearranging the expression. A corner, jump or undefined value at the point can prevent a derivative from existing.

ONE TOOL, DIFFERENT TASKS

Choose the mode for your calculation

Scientific Calculator

Powers, roots, logarithms, trigonometry, factorials, combinations and permutations. Decimal and exact arithmetic fraction displays, Ans and memory.

Complex Number Calculator

Calculate with i. Read the rectangular result, magnitude, argument and conjugate. Angle units apply to the argument and trigonometric functions.

Matrix Calculator

Add, subtract and multiply matrices up to 4 × 4. Find a determinant, inverse or transpose. Matrix B is needed only for binary operations.

Numerical Calculus Calculator

Approximate a definite integral or a derivative at a real point. This is numerical calculus; it does not produce symbolic antiderivatives.

Equation Solver

Solve a quadratic, including complex roots, or a system of two or three simultaneous linear equations. Degenerate quadratic inputs are handled as linear equations.

Statistics Calculator

Find count, sum, mean, median, range endpoints, variance and standard deviation for up to 1,000 values. Choose sample or population statistics.

Base-N Calculator

Convert signed integers of up to 128 bits between binary, octal, decimal and hexadecimal. Bitwise operations use unsigned 32-bit operands.

Function Table Calculator

Evaluate a real-valued function over a range of x values. Choose start, end and step; each table supports up to 201 rows.

TRY IT YOURSELF

Numerical Calculus Calculator worked examples

Integrate a polynomial

∫₀³ x² dx

Approximately 9

The reference antiderivative is x³/3. Evaluating at 3 and 0 gives 27/3−0=9.

Differentiate a cubic at a point

Derivative of x³ at x=2

Approximately 12

The reference derivative is 3x². At x=2, this is 3×4=12.

Integrate a sine function

∫₀^π sin(x) dx, RAD

Approximately 2

Using the reference antiderivative −cos(x), the difference is −cos(π)+cos(0)=2.

READ THE RESULT WITH CONTEXT

Accuracy, notation and limits

Use sufficiently smooth real-valued functions. The reported estimated difference is not a guaranteed error bound: an unsampled discontinuity, narrow peak or rapidly oscillating function can defeat numerical sampling. Split difficult intervals and compare against an independent result.

RAD is the default on this page. DEG also works, but differentiating sin(x) with x measured in degrees includes the π/180 scale factor. Infinite limits, symbolic integration and complex-valued integrands are not supported.

Read our calculation methodology ↗

COMMON QUESTIONS

Numerical Calculus Calculator FAQs

Does this show symbolic calculus steps?

No. It estimates definite integrals and derivatives at numeric points. It does not return indefinite integrals or symbolic derivative expressions.

Why should I check the angle setting?

The function uses the selected unit. In RAD, the derivative of sin(x) at 0 is 1. In DEG, it is π/180 because the input represents degrees.

Can I integrate across a singularity?

Do not treat a sampled result across a singularity as reliable. This calculator rejects sampled undefined values, but cannot guarantee detection of every singularity. Analyze the function and use an appropriate mathematical method.

Calculation library: math.js. This page is an independent CalcPebble tool.