Graphing Calculator
Plot mathematical functions and visualise equations for GCSE, A-Level and beyond
Last updated: February 2026
Function Plotter
Supported Mathematical Functions
This graphing calculator supports all functions required for GCSE and A-Level Mathematics. Enter expressions using the syntax below:
| Function | Syntax | Example | Description |
|---|---|---|---|
| Power | x^n |
x^2, x^3 |
Raises x to the power n |
| Square Root | sqrt(x) |
sqrt(x+1) |
Square root function |
| Sine | sin(x) |
2*sin(x) |
Trigonometric sine (radians) |
| Cosine | cos(x) |
cos(2*x) |
Trigonometric cosine (radians) |
| Tangent | tan(x) |
tan(x) |
Trigonometric tangent (radians) |
| Inverse Trig | asin(x), acos(x), atan(x) |
asin(x) |
Inverse trigonometric functions |
| Natural Log | log(x) |
log(x+1) |
Natural logarithm (ln) |
| Exponential | exp(x) |
exp(-x^2) |
e raised to the power x |
| Absolute Value | abs(x) |
abs(x-2) |
Modulus function |x| |
| Constants | pi, e |
sin(pi*x) |
π ≈ 3.14159, e ≈ 2.71828 |
Syntax Tips
- Multiplication: Use
*explicitly, e.g.,2*xnot2x - Powers: Use
^for exponents, e.g.,x^2for x squared - Brackets: Use parentheses for grouping, e.g.,
(x+1)^2 - Trigonometry: All trig functions use radians (multiply by
pi/180for degrees)
Common Graph Types for UK Exams
Click on any example to plot it instantly:
GCSE Mathematics
A-Level Mathematics
Advanced Functions
Understanding Graph Features
Key Points
Roots/Zeros: Where the graph crosses the x-axis (y = 0)
Y-intercept: Where the graph crosses the y-axis (x = 0)
Turning points: Where the gradient changes from positive to negative or vice versa
Graph Transformations
y = f(x) + a: Vertical shift up by a
y = f(x + a): Horizontal shift left by a
y = af(x): Vertical stretch by factor a
y = f(ax): Horizontal compression by factor a
Symmetry
Even functions: f(-x) = f(x), symmetric about y-axis (e.g., x², cos(x))
Odd functions: f(-x) = -f(x), rotational symmetry about origin (e.g., x³, sin(x))
Asymptotes
Vertical: Line x = a where function → ±∞ (e.g., 1/x at x = 0)
Horizontal: Line y = b that graph approaches as x → ±∞
UK Exam Board Tips
This graphing calculator is aligned with UK exam specifications:
- AQA, Edexcel, OCR GCSE: Practice quadratics, cubics, reciprocals, and trigonometric graphs
- A-Level Pure Maths: Explore exponentials, logarithms, and composite functions
- Further Maths: Investigate polar coordinates, parametric equations, and complex functions
- Exam technique: Practise sketching key features (roots, asymptotes, turning points) before using this tool to check your work
Important Notes
- Trigonometry: All angles are in radians. For degrees, multiply by π/180
- Logarithms:
log(x)is the natural log (ln). For log₁₀, uselog(x)/log(10) - Division by zero: Functions like 1/x will show gaps at x = 0
- Exam calculators: This online tool is for revision only - check your exam board's approved calculator list
Using Graphing Calculators in UK Maths Education
Graphing calculators play an increasingly important role in UK mathematics education, particularly at GCSE and A-Level. Understanding how to visualise functions gives students deeper mathematical insight than working with equations alone.
GCSE Maths: Graph Skills Required by UK Exam Boards
All major UK exam boards -- AQA, Edexcel (Pearson), OCR, and WJEC -- require students to recognise, sketch, and interpret graphs of standard functions. At GCSE Higher tier, students must be able to:
- Identify graph shapes -- recognise quadratic (parabola), cubic, reciprocal, exponential, and trigonometric curves from their equations
- Find key features -- locate roots (where y = 0), the y-intercept (where x = 0), turning points, and lines of symmetry
- Apply transformations -- understand how y = f(x) + a, y = f(x + a), y = af(x), and y = f(ax) shift and stretch graphs
- Estimate solutions graphically -- read approximate values from plotted curves, including solving simultaneous equations by finding intersection points
This online graphing tool lets you practise all of these skills. Plot a function, then check your hand-drawn sketch against the computer-generated version to build confidence before your exam.
A-Level Mathematics: Advanced Graphing Techniques
At A-Level, students explore more sophisticated functions and are expected to understand their behaviour analytically. Key topics where this graphing calculator helps include:
- Differentiation and gradient -- visualise how the gradient of a curve changes by plotting the original function alongside its derivative
- Integration and area -- understand definite integrals as the area under a curve between two limits
- Trigonometric identities -- plot sin(x), cos(x), and tan(x) together to observe their relationships, periods, and asymptotes
- Exponential modelling -- compare exponential growth (ex) and decay (e-x) curves used in real-world problems such as population growth and radioactive decay
- Composite and inverse functions -- see how f(g(x)) differs from g(f(x)), and how a function and its inverse reflect in the line y = x
Practical Revision Tips for UK Students
To get the most out of this graphing calculator during your revision:
- Sketch first, then verify -- draw the graph by hand based on the equation, then plot it here to check your sketch. This builds the skill examiners test.
- Explore transformations systematically -- start with y = x2, then try y = x2 + 3, y = (x + 3)2, and y = 2x2 to see each transformation type in action.
- Use multiple functions -- plot two functions simultaneously to practise finding intersection points, which is how simultaneous equations are solved graphically.
- Check asymptote behaviour -- for functions like 1/x and tan(x), zoom in near the asymptotes to understand why the function cannot be evaluated at certain points.
Remember that while graphing calculators are invaluable for revision, most UK exam boards do not permit online tools during exams. Check your exam board's approved calculator list on the JCQ website to confirm which calculator you may use in the examination hall.
Frequently Asked Questions
Enter your function in the input field using standard mathematical notation. For example, enter 'x^2' for x squared, 'sin(x)' for sine, or '2*x + 3' for a linear function. Click 'Add Function' to plot it on the graph. You can adjust the viewing window using the X Min, X Max, Y Min, and Y Max fields.
The calculator supports polynomial (x^n), trigonometric (sin, cos, tan and their inverses), exponential (exp), logarithmic (log - natural log), square root (sqrt), and absolute value (abs) functions. You can also use the constants pi (π) and e (Euler's number). Use * for multiplication and ^ for powers.
Yes, you can plot multiple functions simultaneously. Each function will be displayed in a different colour. Use the checkboxes next to each function to show or hide them, and the × button to remove them completely. This is useful for comparing graphs or exploring transformations.
Yes, this graphing calculator supports all functions required for GCSE and A-Level Mathematics. It's ideal for visualising quadratic, cubic, trigonometric, and exponential graphs covered in AQA, Edexcel, OCR, and WJEC specifications. Use it to check your sketch work and understand graph transformations.
The tangent function has vertical asymptotes at x = π/2, 3π/2, etc. (approximately 1.57, 4.71 radians). At these points, tan(x) approaches infinity, so the graph cannot be drawn. This is mathematically correct behaviour - the function is undefined at these points.
This calculator uses radians for all trigonometric functions. To convert degrees to radians, multiply by π/180. For example, to plot sin(30°), enter sin(30*pi/180). Remember: 180° = π radians, 90° = π/2 radians, 360° = 2π radians.
Currently, you can take a screenshot of your graph using your device's screenshot function (Print Screen on Windows, Cmd+Shift+4 on Mac). The graph is displayed on an HTML5 canvas which renders in high quality for educational use.
Check your syntax carefully. Common issues include: forgetting to use * for multiplication (write 2*x not 2x), using the wrong bracket types (use parentheses only), or having undefined values in your domain. For functions like log(x) and sqrt(x), ensure x > 0 as they're undefined for negative values.
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Pro Tips for Accurate Results
- Double-check your input values before calculating
- Use the correct unit format (metric or imperial)
- For complex calculations, break them into smaller steps
- Bookmark this page for quick future access
Understanding Your Results
Our Calculator Graphing provides:
- Instant calculations - Results appear immediately
- Accurate formulas - Based on official UK standards
- Clear explanations - Understand how results are derived
- 2025/26 updated - Using current rates and regulations
Common Questions
Is this calculator free?
Yes, all our calculators are 100% free to use with no registration required.
Are the results accurate?
Our calculators use verified formulas and are regularly updated for accuracy.
Can I use this on mobile?
Yes, all calculators are fully responsive and work on any device.