Numerical Differentiation Calculator

Approximate derivatives with forward, backward, central and five-point differences and compare with the symbolic value.

Your result will appear here

Fill in the fields and press Calculate, or pick one of the examples.

About the Numerical Differentiation Calculator

Approximates the derivative of a function at a point with finite differences: forward, backward, central and the five-point stencil. When the function can also be differentiated symbolically, the true value and each method’s error are shown.

Limitations

Too small a step amplifies rounding error; too large a step increases truncation error.

How to use it

Type the function and the point x.
Choose a step size h.
Press Calculate and compare the methods.

Example

sin(x) at x = 0, h = 0.001

→ Central difference ≈ 0.999999833333

Formulas used

f'(x) \approx \frac{f(x + h) - f(x - h)}{2h}

Central difference, error of order $h^2$ .

f'(x) \approx \frac{f(x + h) - f(x)}{h}

Forward difference, error of order $h$ .

Derivative CalculatorDifferentiate functions symbolically — first, second and higher derivatives — with the rules used and a numerical verification.Numerical Integration CalculatorApproximate integrals with the trapezoidal, midpoint and Simpson’s rules and compare them with an adaptive reference value.

About the Numerical Differentiation Calculator

Limitations

How to use it

Formulas used

Related tools

About the Numerical Differentiation Calculator

Limitations

How to use it

Formulas used