Scientific Calculator & Function Grapher

Advanced scientific calculator, interactive function plotter, derivatives, numerical integrals, and equation solver for students.

Scientific calculator and graph plotter: how it computes

The tool combines a scientific calculator, a four-curve plotter, an equation solver (quadratic, cubic, 2 × 2 linear system) and descriptive statistics. Roots, extrema, derivative and integral are found numerically: a 400-point scan, a central difference and Simpson’s rule over 200 subintervals.

Methods used

  • Roots: the active curve is evaluated at 400 points across the visible window; each sign change gives a root by linear interpolation (up to 5).
  • Extrema: a point higher (or lower) than both neighbours is kept as a local maximum (or minimum).
  • Derivative and tangent: f′(x₀) ≈ (f(x₀ + h) − f(x₀ − h)) / 2h with h = 10⁻⁵.
  • Integral: Simpson’s 1/3 rule over 200 subintervals between a and b.
  • Equations: discriminant Δ = b² − 4ac for quadratics, Cardano’s method (depressed form t³ + pt + q) for cubics, determinants for a 2 × 2 system.
  • Statistics: variance divides by n (population variance); Q1 and Q3 are read at positions ⌊0.25 n⌋ and ⌊0.75 n⌋ of the sorted data.

Examples

∫₀³ x² dx returns 9, exact because Simpson’s rule integrates polynomials up to degree 3 without error. x² − 5x + 6 = 0: Δ = 1, roots 2 and 3. Default data (12, 15, 8, 20, 14, 18, 11, 16, 19, 13): mean 14.6, median 14.5, variance 12.84, standard deviation 3.58 (3.78 for the sample standard deviation, divided by n − 1, which the tool does not compute).

Limits

Trigonometric functions follow the selected unit, degrees by default, in the plotter too. A double root with no sign change (x² at 0) can be missed by the scan. Constants in scientific notation inserted from the panel (G, h, N_A…) are read as a single number, as is an entry such as 1e-5: 6.62607015e-34 equals 6.62607015 × 10⁻³⁴.

Sources and dates: CODATA physical constants; h, N_A, k_B and e have been exact since the SI revision of 20/05/2019 (c since 1983); electron mass 9.1093837139 × 10⁻³¹ kg per NIST, CODATA 2022 values. (checked 14/10/2026)

Frequently Asked Questions

How does the calculator compute an integral?

With Simpson’s 1/3 rule over 200 subintervals between bounds a and b. For a polynomial of degree 3 or less the result is exact: ∫₀³ x² dx returns 9.

Why does sin(90) give 1 rather than 0.894?

The default angle unit is degrees: sin(90°) = 1. In radians, sin(90) is about 0.894. The DEG, RAD or GRAD setting also applies to plotted curves.

Is the standard deviation shown for a population or a sample?

For a population: the variance divides by n. For the data 12, 15, 8, 20, 14, 18, 11, 16, 19, 13 the tool shows 3.58; the sample standard deviation (divided by n − 1) would be 3.78.

How do I solve a cubic equation?

Enter a, b, c and d of ax³ + bx² + cx + d = 0 (a non-zero). The tool reduces it to t³ + pt + q and applies Cardano’s method, or the trigonometric form when there are three real roots.

Is this tool really free?

Yes, all tools on Kristools are 100% free and accessible without registration.

Is my data protected?

Yes. All processing is performed directly and securely inside your browser. No personal data is sent to our servers.