Linear
Straight line
y = 2x + 3
The graph of y = mx + c is a straight line with gradient m and y-intercept c. A positive m slopes upwards, a negative m slopes downwards, and m = 0 gives a horizontal line.
Free online tool
Online Graphing Calculator
Plot any equation in seconds. Type y = x^2 - 4 and the curve appears instantly — then pan, zoom, trace exact coordinates, add sliders for parameters, and read off roots, intercepts, turning points and intersections. Free, unlimited and works on phone, tablet and desktop.
Key points of y = x^2 inside the visible window (-10 ≤ x ≤ 10). Pan or zoom to search a different range.
Roots (x-intercepts)
- x = 0
y-intercept
- y = 0
Turning points
- Min (0, 0)
Intersections
No crossing with another curve
Enter a value of x
Graph calculators by equation type
Each page below opens this calculator pre-loaded with the right equation, and explains the maths — key formulas, worked examples and the questions students actually ask.
Parabola Graph Calculatory = a x^2 + b x + cStraight Line Graph Calculatory = m x + cCubic Graph Calculatory = x^3 - 3xSine Graph Calculatory = a sin(b x + c)Cosine Graph Calculatory = a cos(b x + c)Tangent Graph Calculatory = a tan(b x)Exponential Graph Calculatory = 2^xLogarithmic Graph Calculatory = ln(x)Absolute Value Graph Calculatory = a |x - h| + kRational Function Graph Calculatory = 1/xCircle Graph Calculator — Plot a Circle Onliner = 5Ellipse Graph Calculator — Plot x²/a² + y²/b² = 1y = b sqrt(1 - x^2/a^2)Hyperbola Graph Calculator — Plot x²/a² − y²/b² = 1y = 3 sqrt(x^2/16 - 1)Polar Graph Calculatorr = 4 sin(k θ)Normal Distribution Graph Calculatory = (1/(s sqrt(2pi))) e^(-((x - m)^2)/(2 s^2))Solve Equations Graphically — Intersection Calculatory = x^2 - 2
What is an online graphing calculator?
An online graphing calculator is a browser-based tool that draws the graph of a mathematical equation and lets you explore it interactively. You type a function such as y = x² − 4, and it plots the curve on a coordinate grid, calculates the points that matter — roots, intercepts, maxima and minima — and lets you zoom, trace and compare several functions at once. Unlike a handheld graphing calculator it costs nothing, needs no installation, and shows a full-colour graph as large as your screen.
This calculator supports four kinds of input: functions of x (y = sin(x)), functions of y (x = y^2), polar equations (r = 2 + 2cos(θ)) and single points ((3, -2)). Every calculation happens in your browser, so results are instant and your work is never uploaded to be solved.
- Cost
- Free, no signup
- Equations at once
- Up to 12
- Works on
- Phone, tablet, laptop
- Angle units
- Radians or degrees
How to use the graphing calculator
- 1
Type your equation
Click the first row and type an equation such as y = x^2 - 4. The graph updates as you type. You can leave off the "y =" if you prefer.
- 2
Add more curves
Press Enter or click "Add equation" to plot up to 12 equations together, each in its own colour. Use the eye icon to hide a curve without deleting it.
- 3
Move around the graph
Drag to pan, scroll or pinch to zoom, and double-click to zoom in on a point. Use the reset button to return to the standard −10 to 10 window.
- 4
Add sliders for parameters
Use letters such as a, b or k in the equation — for example y = a sin(b x) — and a slider appears for each. Drag it, or press play to animate it.
- 5
Read the key points
Open the Key points tab for roots, the y-intercept, turning points and intersections, or the Table tab for a table of values. Hover or tap any curve to trace exact coordinates.
- 6
Save or share the graph
Download the graph as a PNG image, or copy the shareable link — it reopens the calculator with your exact equations, sliders and zoom level.
How to type equations — syntax guide
Type maths the way you write it. Capital letters, spaces and Unicode symbols pasted from a textbook (× ÷ − √ π ²) are all understood, and the × between a number and a variable is optional.
Equation forms
| Type this | What it draws |
|---|---|
| y = x^2 - 4 | A function of x — the usual case. The bare form x^2 - 4 works too. |
| f(x) = 2x + 1 | Function notation, treated exactly like y = 2x + 1. |
| x = y^2 - 3 | A function of y, drawn sideways. Use it for sideways parabolas. |
| x = 4 | A vertical line at x = 4. |
| r = 2 + 2cos(θ) | A polar curve. θ and t mean the same thing here. |
| (3, -2) | A single plotted point. Both coordinates may be expressions, e.g. (a, a^2). |
Operators and notation
| Notation | Meaning |
|---|---|
| + - * / | Add, subtract, multiply, divide |
| 2x, 3(x+1), 2sin(x) | Implicit multiplication — the × is optional |
| x^2, x^(1/3) | Powers, including fractional and negative exponents |
| |x - 2| | Absolute value (modulus) |
| 5! | Factorial — works on decimals too, via the gamma function |
| x % 3 | Remainder after division |
| pi, e, tau, phi | Built-in constants π, e, τ and the golden ratio φ |
| 1e-3 | Scientific notation for 0.001 |
Supported functions
Trigonometry
| Function | What it does |
|---|---|
| sin(x), cos(x), tan(x) | The three basic ratios |
| csc(x), sec(x), cot(x) | Reciprocal ratios |
| asin(x), acos(x), atan(x) | Inverses — arcsin, arccos and arctan also work |
| sinh(x), cosh(x), tanh(x) | Hyperbolic functions, with asinh, acosh and atanh |
| atan2(y, x) | Angle of the point (x, y) from the positive x-axis |
Powers, roots and logs
| Function | What it does |
|---|---|
| sqrt(x), cbrt(x) | Square root and cube root |
| root(x, n) | The nth root of x — root(-8, 3) correctly gives −2 |
| exp(x) | e raised to the power x |
| ln(x) | Natural logarithm (base e) |
| log(x) | Logarithm base 10 |
| log(x, b), log2(x), log10(x) | Logarithm of x to base b, base 2, base 10 |
Rounding and comparison
| Function | What it does |
|---|---|
| abs(x), sign(x) | Magnitude and sign (−1, 0 or 1) |
| floor(x), ceil(x), trunc(x) | Round down, round up, cut off the decimals |
| round(x), round(x, 2) | Round to the nearest whole number or to 2 decimal places |
| fract(x) | Fractional part of x |
| min(a, b, …), max(a, b, …) | Smallest and largest of any number of values |
| mod(a, b) | Modulo that always returns a non-negative result |
Numbers and combinatorics
| Function | What it does |
|---|---|
| gcd(a, b), lcm(a, b) | Highest common factor and lowest common multiple |
| hypot(a, b) | Length of the hypotenuse, √(a² + b²) |
| ncr(n, r), npr(n, r) | Combinations and permutations |
| factorial(x), gamma(x) | Factorial and the gamma function |
| pow(a, b) | Same as a^b |
What you can plot — every common graph, with the equation to type
The shapes that appear most often in Class 11 and 12 mathematics, engineering entrance papers and first-year university courses — with a worked example you can paste straight into the calculator above.
Quadratic
Parabola
y = x^2 - 4x + 3
Every quadratic y = ax² + bx + c draws a parabola. It opens upwards when a > 0 and downwards when a < 0. The vertex sits at x = −b/2a, and the roots shown in the Key points tab are the solutions of the equation.
Cubic
Cubic curve
y = x^3 - 3x
A cubic can cross the x-axis up to three times and usually has one local maximum and one local minimum — both listed as turning points once you plot it.
Absolute value
Modulus graph
y = |x - 2| - 3
Absolute value graphs make a sharp V. The vertex is where the bracket equals zero, so y = |x − 2| − 3 has its corner at (2, −3).
Trigonometric
Sine and cosine waves
y = 2sin(3x)
In y = a·sin(bx + c), a is the amplitude, the period is 2π/b, and c shifts the wave left or right. Turn on π-axis labels in Graph settings to read the period straight off the x-axis.
Trigonometric
Tangent curve
y = tan(x)
tan(x) repeats every π and has a vertical asymptote at every odd multiple of π/2, where cos(x) = 0 and the function is undefined.
Exponential
Exponential growth and decay
y = 2^x
Exponential curves pass through (0, 1) and never touch the x-axis. Use y = e^(-0.5x) for decay — the classic shape for half-life, cooling and depreciation problems.
Logarithmic
Logarithm
y = ln(x)
The logarithm is only defined for x > 0, so the curve simply stops at the y-axis. It is the mirror image of y = eˣ in the line y = x.
Reciprocal
Rational function
y = 1/(x - 2)
A denominator that hits zero creates a vertical asymptote — here at x = 2. The calculator draws the two branches separately instead of joining them with a false vertical line.
Polar
Circle and cardioid
r = 2 + 2cos(θ)
Polar equations describe distance from the origin as the angle turns. r = 5 is a circle of radius 5; r = a + a·cos θ is the heart-shaped cardioid; r = a·sin(kθ) draws a rose.
Statistics
Normal distribution
y = (1/(s sqrt(2pi))) e^(-((x - m)^2)/(2 s^2))
The bell curve of statistics. Sliders m and s let you move the mean and stretch the standard deviation to see how the spread changes.
Problem solving
Solving equations graphically
y = x^2 - 2 and y = x + 4
Plot both sides of an equation as separate curves — the x-coordinates of the intersections are the solutions. The Key points tab lists them for you.
Reading a graph: roots, intercepts, turning points and asymptotes
- Root (x-intercept)
- A value of x where the curve crosses or touches the x-axis, so f(x) = 0. Roots are the solutions of the equation f(x) = 0, and the Key points tab finds every one inside the visible window.
- y-intercept
- The value of the function at x = 0 — where the curve crosses the vertical axis. For y = ax² + bx + c it is always c.
- Turning point (maximum or minimum)
- A point where the curve stops rising and starts falling, or the reverse. At a turning point the gradient dy/dx is zero, which is why they are also called stationary points.
- Vertical asymptote
- A vertical line the curve approaches but never reaches, caused by a denominator going to zero — as in y = 1/(x − 2) at x = 2. The calculator breaks the line there instead of drawing a false vertical stroke.
- Horizontal asymptote
- A horizontal level the curve settles towards as x grows very large or very negative. Zoom out to see it: y = 1/x flattens onto y = 0.
- Intersection
- A point shared by two curves. The x-coordinate of an intersection solves the equation f(x) = g(x), which makes plotting both sides the quickest way to solve an equation graphically.
- Domain
- The set of x values for which the function is defined. Gaps in the drawn line mark values outside the domain — y = ln(x) simply stops at x = 0.
- Period and amplitude
- For a wave y = a·sin(bx), the amplitude a is half the vertical distance between crest and trough, and the period 2π/b is the horizontal distance before the pattern repeats.
Online graphing calculator vs a handheld graphing calculator
| Feature | This online calculator | Handheld (Casio / TI) |
|---|---|---|
| Cost | Free, unlimited use | ₹1,500 – ₹15,000 for a graphing model |
| Screen | Full colour, as large as your display | Small monochrome or low-resolution colour LCD |
| Curves at once | Up to 12, colour-coded | Typically 4 – 10, one line style |
| Sliders and animation | Automatic for any parameter, with play/pause | Rarely available |
| Sharing work | PNG download and a link that restores the graph | Photograph the screen |
| Allowed in exams | No — internet devices are not permitted | Only if your board or university allows that model |
| Best for | Homework, revision, checking answers, teaching | Sitting the actual examination |
Note: internet-connected devices are not permitted in Indian board examinations or in competitive exams such as JEE, NEET and CUET. Use this calculator for study, homework and checking your working.
Frequently asked questions
Is this online graphing calculator free?
Yes. The graphing calculator on MyInternships.in is completely free, with no signup, no download and no limit on how many graphs you plot. All the maths runs inside your browser — your equations are never sent to a server to be solved, so plotting stays instant even on a slow connection.
How do I plot a graph online?
Type an equation such as y = x^2 - 4 into the first row and the curve appears instantly. Press Enter to add another equation, drag the graph to move around, and scroll or pinch to zoom. Every equation gets its own colour.
How many graphs can I plot at the same time?
Up to 12 equations at once. Each row has a colour swatch you can click to change the colour, an eye button to hide the curve without deleting it, and a delete button.
How do I find the roots and turning points of a function?
Open the "Key points" tab under the graph. It lists the roots (x-intercepts), the y-intercept, every local maximum and minimum, and the points where the selected curve crosses the other curves — all calculated numerically for the part of the graph you can currently see. Pan or zoom to search a wider range.
Can it plot a circle or an implicit equation like x² + y² = 25?
Not directly — this calculator plots explicit equations. There are two easy ways round it: plot the circle in polar form as r = 5, or plot the two halves separately as y = sqrt(25 - x^2) and y = -sqrt(25 - x^2).
Does it support polar graphs?
Yes. Type r = 2 + 2cos(θ) for a cardioid or r = 4sin(5θ) for a rose curve. You can type t instead of θ if that is easier, and the "Polar turns of θ" setting lets a spiral sweep up to 12 full revolutions.
Does the calculator use radians or degrees?
Radians by default, which is the standard for graphing trigonometric functions. Switch the RAD/DEG toggle above the graph to work in degrees — sin(90) then equals 1 instead of 0.894.
What are the sliders for?
Any letter in your equation that is not x, y, r, t or θ automatically becomes a slider. Type y = a sin(b x + c) and you get three sliders for amplitude, frequency and phase shift. Press the play button beside a slider to animate it and watch the curve move.
Can I use the graphing calculator on a phone?
Yes. Drag with one finger to pan, pinch with two to zoom, and tap a curve to read its coordinates. The on-screen keypad gives you brackets, powers, roots, π and the trigonometric functions without hunting through the phone keyboard.
Can I save or share my graph?
Both. The download button saves the graph as a PNG image, and the link button copies a URL that reproduces your exact equations, sliders and zoom level — useful for sending a question to a teacher or classmate.
Which functions and operators can I use?
Arithmetic (+ − × ÷ ^ % !), brackets, |absolute value|, all six trigonometric functions and their inverses, hyperbolic functions, sqrt, cbrt, exp, ln, log, log2, log10, abs, sign, floor, ceil, round, min, max, mod, gcd, lcm, hypot, gamma, nCr and nPr, plus the constants π, e, τ and φ. Implicit multiplication works, so 2x, 3(x+1) and 2sin(x) all parse the way you expect.
Why does tan(x) draw a gap instead of a vertical line?
Because there is no line there. tan(x) has a vertical asymptote at every odd multiple of π/2, where the function is undefined. The calculator detects the jump and lifts the pen rather than drawing a false vertical stroke — the same reason y = 1/x is drawn as two separate branches.
Can I use this instead of a Casio or TI graphing calculator?
For homework, revision and checking answers, yes — it plots, traces, tabulates and finds key points the same way. For an examination you must use whatever physical calculator your board or university permits, because internet-connected devices are not allowed in Indian board exams or in competitive exams like JEE.
Does it work for JEE, NEET and board exam preparation?
Yes. Plotting a function is one of the fastest ways to understand transformations, asymptotes, domain and range, and the shape of conics and trigonometric curves that appear in Class 11 and 12 mathematics and in JEE Main and Advanced.
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