Graphing calculator

Typing formulas

• Fraction: type /; the cursor moves to the denominator. Press → to leave it before carrying on (3/4, then →, then +1).
• Power: ^ or the x² key; → to come back to the line.
• Root: type sqrt or use the √ key; n-th root with its own key.
• Functions: type sin, cos, ln, exp… directly; pi gives π and oo gives infinity ∞ (handy for integral bounds).
• Up arrow ↑ in an empty field recalls the last calculation.
• Fixing mistakes: ⌫ first removes “dx”, then the whole integral (or sum) with its bounds once it is empty; hold it to keep deleting. ↶ undoes, AC or Esc clears the input.

Exact or decimal?

Each answer is given as an exact value when possible, followed by its decimal value:

• √12 + √27 = 5√3 ≈ 8.660254038
• 1/(1 + √2) = √2 − 1 (the denominator is rationalised)
• cos(π/12) = (√6 + √2)/4
• 0.1 + 0.2 = 3/10 = 0.3: no rounding error, unlike many software calculators

When no simple exact form exists (ln 2, sin 1, √(1+√2)…), only the decimal value is shown, with the number of digits you choose (6 to 15).

Integrals, sums and products

• Integral: ∫ key, then the bounds (Tab moves between them) and the function. The variable is whatever follows “d”: dx, dt, du, dθ… Example: ∫₀¹ x² dx = 1/3 (exact for polynomials), ∫₀^π sin t dt = 2.
• Infinite bounds (… key then ∞, or type oo): ∫ from −∞ to +∞ of e^(−x²) dx ≈ 1.772453851 (= √π). A divergent integral, such as ∫₁^∞ 1/x dx, is flagged.
• Double integrals: ∫₀¹ ∫₀¹ xy dy dx = 0.25; the inner bound may depend on the outer variable.
• Sum and product: Σ and Π keys, with any index under the symbol (k=1, i=0, n=1…). Σ k for k from 1 to 100 = 5,050; Π j for j from 1 to 5 = 120; Σ 1/2^i for i from 0 to 5 = 63/32.

Variables and functions

• a=5 creates the variable a (one letter, except x and e). It appears in the Variables panel and works in every calculation and function (f(x)=ax+1).
• Ans recalls the last answer; click an answer in the history to insert it; click a calculation to copy it for editing.
• Functions defined in the graph tab can be used in calculations: f(3), and even f'(3) for the derivative at a point, exactly when possible.

Studying a function

1. Enter f(x), for example x² − 2x − 3: the exact derivative f′(x) = 2x − 2 appears below it.
2. The graph shows the curve; “Plot derivatives” adds f′ as a dashed line.
3. Key points in the window are listed and marked: zeros (−1 and 3), minimum (1, −4), intersections between curves.
4. Hover over a curve to read x, f(x) and the slope of the tangent there.
5. The Table of values tab gives f(x) from a chosen start and step, to export as CSV or print.

Equations and systems

• Equation: type it as is (x² − 2x − 3 = 0, eˣ = 3, cos x = x). Up to degree 2, solutions are exact, with Δ: x² − 2 = 0 gives x = ±√2; x² + x + 1 = 0 gives the complex solutions −1/2 ± (√3/2)i. Beyond that, all roots of the polynomial are given, exactly when they are simple fractions (x³ − 6x² + 11x − 6 = 0 → 1, 2, 3). Other equations are solved numerically on the chosen interval.
• Polynomial: enter the coefficients, even as calculations (1/3, √2, a…).
• Linear system with 2 to 5 unknowns: exact Gaussian elimination; the tool reports systems with no solution or infinitely many.

Sequences

• Explicit (u_n = 3n + 2) or recursive: choose the computed term (u_n+1, u_n or u_n+2) and express it with earlier terms, e.g. u_n+1 = 0.5u_n + 3, u_n = u_n−1 + 2n or u_n+2 = u_n+1 + u_n (Fibonacci).
• The order of the recurrence is detected automatically and the number of initial terms adapts (two for Fibonacci, three for an order-3 recurrence…).
• Up to three sequences, each with a letter of your choice (u, v, w, a, b…). A sequence may use another one: v_n+1 = v_n + u_n.
• Table of terms, scatter plot and cobweb (staircase or spiral) for a recursive sequence.
• Detected type (arithmetic, geometric), long-term behaviour (“seems to converge to 6”), sum of terms.
• Threshold: smallest n with u(n) > 5.9, with the matching Python algorithm.
• In the Calculations tab, u(10) gives the 10th term directly.

Statistics and regression

• Four lists L1 to L4. Paste one or more columns copied from a spreadsheet: they fill the lists. Enter or ↓ moves to the next row.
• One variable (with optional frequencies): mean, median, quartiles, deciles, standard deviation σ and s, variance, range, mode, box plot and chart. Quartiles follow the French school method or the spreadsheet (interpolation) method.
• Two variables: scatter plot and linear, proportional, exponential, power, logarithmic or polynomial (degree 2 or 3) regression, with r, R², mean point and prediction. “Send to Functions” adds the model to the graph tab.

Probability

Binomial, geometric, Poisson, hypergeometric, uniform, normal and exponential distributions: P(X = k), P(X ≤ k), P(a ≤ X ≤ b), quantiles, mean and variance, chart, fluctuation interval and the equivalent TI and Casio calculator functions.

Moving between modules

• Under each result: → Calc inserts it into the input (exactly when possible), ＋ History adds it to the history with the module's name (it becomes Ans), Store saves it in a variable, ⧉ copies the value.
• Module fields accept calculations and variables: p = 1/4, n = a, x = Ans…
• Example: solve a system, store x as p, then use it as the parameter of a binomial distribution.

Good to know

• Set the angle unit at the top right (radians, degrees or gradians): sin(30) is 1/2 in degrees but about −0.988 in radians. The ° symbol forces degrees whatever the unit, and inverse functions give the exact angle in the chosen unit (arcsin(1/2) = 30° or π/6). A small badge in the history shows which unit was used.
• The ⚙ Options menu sets the display: exact and decimal, exact only or decimal only; automatic, scientific or engineering notation (12,345.678 → 12.345678 × 10³); number of significant digits.
• Key points are found numerically within the visible window: widen the window to find others.
• This tool is not allowed in exams, which require a calculator in exam mode. It is for learning, checking exercises and preparing documents (LaTeX export of the history, graph image).
• For more advanced graphs (parameter sliders, interpolation, TikZ export), also try the function grapher.

Guide written and checked by Erwan Hautot · updated 6 November 2026.