TOOL 05 / GRAPH

A graphing calculator that does the analysis too.

Q: Can it plot implicit equations and inequalities?

Yes. Type an equation in x and y, such as x² + y² = 9, for the curve, or use ≤ or ≥ to shade the region.

Plot functions, equations, inequalities, parametric and polar curves. Then read off the derivative, the area, the roots and the turning points without leaving the graph.

Open the grapher — Free ↗What it does ↓

No account required · Right in your browser · Works offline once opened

The Slide Rule grapher plotting sine of x and a cubic, with the derivative, the indefinite integral and the points where the curves cross listed beside the plot — Two functions, with the derivative and integral of the first worked out in symbols and its roots, turning points and intersections marked.

WHAT IT DOES

Three graphers under one tab.

Curves in the plane, surfaces in space, and your own measurements, each with the calculations you would otherwise do by hand.

Functions, and much more

Plot sin x, an equation such as a circle, a shaded inequality like x² + y² ≤ 9, a parametric curve (cos 3t, sin 2t) or a polar one, r = 1 + cos θ.

Sliders from spare letters

Type a sin(b x) and a and b become sliders. Drag one and watch the curve respond.

Analysis beside the plot

For any function: the derivative and the indefinite integral in symbols, a definite integral with the area shaded, and the roots, minima, maxima and intersections in view.

3D surfaces

Plot z = f(x, y) and turn it with a drag. Get both partial derivatives, the gradient and tangent plane at a point, and the critical points sorted into maxima, minima and saddles.

Your data, with a fitted curve

Enter a table, plot any column against any other with error bars and log axes, and fit a line, a polynomial, an exponential, a power law, a Gaussian or a function you write yourself.

Results you can quote

A fit reports each parameter with its standard error, R², adjusted R² and the RMSE, shows the residuals, and can be weighted by your error bars.

FROM THE LAB

From a table of readings to a fitted model.

The Data tab is for lab reports. Put in your measurements, choose what goes on each axis, and pick a model. The fitted curve is drawn through the points and the numbers appear underneath, ready to copy as a fit report or as LaTeX.

For the cooling example the fit is y = a·e^(−bx) + c with a = 68.27, b = 0.0774 and c = 21.74, and R² = 0.99993.

On the free plan you type values into the table. Pasting a table straight from Excel or Sheets, saving a graph as an image and exporting CSV are part of Pro.

The Slide Rule grapher fitting an exponential curve with an offset to temperature measurements of a cooling cup of water, with error bars and the fitted curve — The built-in example: a cup of water cooling, fitted with an exponential plus an offset.

IN THREE DIMENSIONS

Turn a function of two variables into something you can hold.

Multivariable calculus is easier to believe when you can see it. Drag to rotate, and the partial derivatives, the gradient and the tangent plane at any point are worked out beside the surface.

The Slide Rule grapher showing the surface z equals sine x times cosine y in three dimensions, with its partial derivatives, gradient and critical points listed — The surface z = sin x · cos y, with its critical points marked and sorted into maxima, minima and saddle points.

TRY THESE

What you can read off a graph.

For f(x) = sin x, plotted in radians, the Analyze panel gives:

YOU ASK FORSLIDE RULE GIVESWHAT IT IS
Derivativef′(x) = cos xIn symbols, and its value at any x: f′(1) = 0.54030231.
Indefinite integral∫ f(x) dx = −cos x + CAlso in symbols, and it can be plotted as a curve of its own.
Definite integral, 0 to 10.4596976941With the area under the curve shaded on the graph.
Roots in viewx = 0, ±3.1415927, ±6.2831853Every crossing of the x-axis in the window.
Intersections(3.15537, −0.0137746) …Where two of your curves meet, here sin x and 0.1x³ − x.

QUESTIONS

Before you open it.

Is the graphing calculator free?

Yes. Plotting, sliders, 3D surfaces, the analysis and curve fitting are all in the free plan. Pro adds saving graphs as images, pasting tables in and CSV export.

Can it plot implicit equations and inequalities?

Yes. Type an equation in x and y, such as x² + y² = 9, for the curve, or use ≤ or ≥ to shade the region.

What can it fit to my data?

Linear, quadratic, cubic, exponential, exponential with an offset, power, logarithmic and Gaussian models, or any function of x you type: every other letter in it becomes a parameter to fit.

Can I put a graph in my report?

Add it to a worksheet as a card that stays live beside your calculations. With Pro, save it as a PNG or export the whole worksheet as a PDF.

One of eight tools that work together.

A value from one goes straight into another

NOTHING TO INSTALL

Give the equation a shape.

Open the grapher — Free ↗

No account required. Free for every tool; Pro adds unlimited worksheets and exports.