📈 6 New Advanced Math Calculators: Graph Functions, Solve Equations, Find Derivatives, Integrals, Limits and T-Tests — Free

The six new calculators at a glance

• Graphing Calculator — plot functions and read off roots, turning points and intercepts.
• Equation Solver — solve linear and quadratic equations step by step.
• Derivative Calculator — differentiate a function and evaluate the slope at a point.
• Integral Calculator — find indefinite and definite integrals, including areas under curves.
• Limit Calculator — evaluate limits, including tricky 0/0 forms, as x approaches a value.
• T-Test Calculator — test whether the difference between two groups is statistically significant.

All six run instantly in your browser, on a phone or a laptop — and each shows its steps, so the method sticks for the exam.

1. Graphing Calculator: see the function, not just the formula

A formula on paper hides its shape. Plot it, and the shape tells the story: where it crosses the axes, where it turns, and where it rises or falls. That is why teachers sketch graphs first and calculate second.

Who it helps: school and college students studying functions, teachers demonstrating a curve live in class, and engineers checking a model before trusting its numbers.

Worked example: plot y = x² − 3x + 2. The graph crosses the x-axis at x = 1 and x = 2 (the roots), and its turning point sits at (1.5, −0.25). If your factorisation gave roots of 1 and 2, the graph confirms it at a glance; if it did not, the graph shows you where to look again.

Try the Graphing Calculator →

2. Equation Solver: from “what is x?” to a checked answer

Equations are the daily bread of algebra, and a single sign slip can wreck an otherwise perfect solution. The Equation Solver handles linear equations and quadratics, showing the working so you can spot exactly where your hand-written attempt diverged.

Who it helps: students from algebra onwards, parents checking homework without relearning the syllabus, and anyone who needs a quick, reliable answer mid-problem.

Worked examples: solve 2x + 5 = 17. Subtract 5 from both sides (2x = 12), then divide by 2: x = 6. For a quadratic, x² − 5x + 6 = 0 factorises as (x − 2)(x − 3) = 0, giving x = 2 or x = 3. Run either through the solver to confirm each step before moving on.

Try the Equation Solver →

3. Derivative Calculator: slopes, rates and turning points

A derivative answers a simple question with wide reach: how fast is this changing, right here? That one idea powers gradients of curves, rates of change in physics and engineering, and the maxima and minima that optimisation problems ask for.

Who it helps: calculus students, A-level and first-year university learners, and engineers working with rates, velocity or growth.

Worked example: differentiate f(x) = 3x³ − 2x² + 5x − 7. Applying the power rule term by term gives f′(x) = 9x² − 4x + 5. At x = 2, the slope is 9(4) − 4(2) + 5 = 36 − 8 + 5 = 33. The calculator gives both the general derivative and the value at your chosen point, so homework and exam practice match.

Try the Derivative Calculator →

4. Integral Calculator: areas, totals and the reverse of differentiation

If a derivative splits a change into instants, an integral adds instants back into a total: the area under a curve, the distance from a velocity graph, or the accumulated quantity behind a rate. It is the second half of calculus, and the half students most often need to double-check.

Who it helps: calculus students, physics and engineering learners, and anyone computing an area or total from a function rather than from a table of numbers.

Worked example: evaluate ∫₀⁴ (2x + 3) dx. An antiderivative is x² + 3x, so the definite integral is (16 + 12) − (0 + 0) = 28. Geometrically, that is the area under the line y = 2x + 3 between x = 0 and x = 4 — a check you can picture as well as calculate.

Try the Integral Calculator →

5. Limit Calculator: what happens as x gets closer — without dividing by zero

Limits are where calculus begins: the value a function approaches, even at a point where it is not defined. The classic trap is a fraction that reads 0/0 at the point of interest. The value is not “undefined” — it is the limit, and finding it is a skill examiners test again and again.

Who it helps: students meeting limits for the first time, and anyone revising continuity, asymptotes or the definition of the derivative itself.

Worked example: find lim_x→2 (x² − 4)/(x − 2). Direct substitution gives 0/0, but factorising the top gives (x − 2)(x + 2)/(x − 2) = x + 2 for x ≠ 2, so the limit is 2 + 2 = 4. The calculator handles the factorisation logic and returns the limit, even when direct substitution fails.

Try the Limit Calculator →

6. T-Test Calculator: is the difference real, or just chance?

Two groups, two averages, one question: is the gap big enough to mean something? A t-test turns sample means, spreads and sizes into a t-value and a p-value, so a conclusion rests on evidence rather than on which average merely looks larger.

Who it helps: statistics and psychology students, researchers and analysts comparing two groups, and teachers showing hypothesis testing with real numbers instead of abstract rules.

Worked example: two classes of 30 students score means of 82 and 76, with standard deviations of 8 and 9. The standard error is √(64/30 + 81/30) ≈ 2.20, so t = (82 − 76) / 2.20 ≈ 2.73. With about 58 degrees of freedom, that gives p ≈ 0.008 — below the usual 0.05 threshold, so the difference is statistically significant. Enter your own groups in the T-Test Calculator and it does the same arithmetic for you.

Try the T-Test Calculator →

Using all six together: a 10-minute study workflow

These tools are strongest as a set. Sketch the function first with the Graphing Calculator, solve any equation it raises with the Equation Solver, then find its slope with the Derivative Calculator, its area with the Integral Calculator, and its behaviour at awkward points with the Limit Calculator. If your coursework then compares two sets of results, finish with the T-Test Calculator.

One habit makes the difference: solve on paper first, then check with the calculator. Used that way, each tool catches slips instead of replacing thinking.