Category
Math Calculators
Math calculators from everyday percentages to algebra and beyond: synthetic division, vertex form, radical equations, Fourier series, and moment of inertia, each with step-by-step working.
Percentage Calculator
Calculate percentages, percent changes, and percent differences with step-by-step solutions.
Moment of Inertia Calculator
Calculate moment of inertia for various geometric shapes including rods, disks, spheres, and rectangular plates with the Parallel Axis Theorem.
ASQ Calculator (Corrected Age & Score)
Calculate corrected age for Ages & Stages Questionnaires (ASQ-3/ASQ:SE-2) and adjust domain scores for omitted answers.
Synthetic Division Calculator
Divide polynomials by linear factors of the form (x - c) using synthetic division. Find the quotient, remainder, and roots step-by-step.
Vertex Form Calculator
Convert quadratic equations between standard form (ax² + bx + c) and vertex form a(x - h)² + k. Find the vertex coordinates and graph properties.
Fourier Series Calculator
Calculate Fourier series coefficients (a₀, aₙ, bₙ) and generate the trigonometric series expansion for any periodic function.
Radical Equation Calculator
Solve equations containing square roots, cube roots, or multiple radicals and identify extraneous roots.
Everyday math: percentages
Most everyday math questions are percentage questions: what is 15% of a bill, what percent one number is of another, or how much a price changed. The Percentage Calculator handles all three and shows the working, which helps when the question is phrased in an unfamiliar way.
Percent change is measured relative to the starting value, so a rise from 50 to 75 is a 50% increase, but a fall from 75 back to 50 is only a 33.3% decrease.
Algebra: polynomials, quadratics, and radicals
The Synthetic Division Calculator divides a polynomial by a linear factor (x − c), giving the quotient and remainder and showing whether c is a root. The Vertex Form Calculator converts quadratics between standard form and vertex form, which reveals the vertex and axis of symmetry directly.
The Radical Equation Calculator solves equations with square or cube roots by isolating and raising both sides to a power, then checks each solution in the original equation. That check matters: squaring both sides can introduce extraneous roots that do not satisfy the original equation.
Advanced topics
The Fourier Series Calculator finds the coefficients that rebuild a periodic function from sines and cosines, a core idea in signal processing. The Moment of Inertia Calculator applies standard formulas for rods, disks, spheres, and plates, with the parallel axis theorem for shifted axes. The ASQ Calculator works out a child’s corrected age for the Ages & Stages Questionnaires, including the prematurity adjustment.
Key formulas
- Percent change
- ((New − Old) ÷ |Old|) × 100
- Vertex from standard form
- h = −b ÷ 2a; k = c − b² ÷ 4a
- Remainder theorem
- P(x) ÷ (x − c) leaves remainder P(c)
- Parallel axis theorem
- I = I_cm + m × d²
Getting accurate results
- For percent change, always divide by the original value, not the new one.
- In synthetic division, write a zero for every missing power of x.
- Always substitute radical-equation solutions back into the original equation.
- A positive a in vertex form means the parabola opens upward and the vertex is a minimum.
Frequently asked questions
- What is the difference between percent change and percentage points?
- Percent change is relative to the starting value. Percentage points are a simple difference between two percentages, such as 5% to 7% being a 2-point rise but a 40% increase.
- When can I use synthetic division?
- Only when dividing by a linear factor of the form x − c. Other divisors need polynomial long division.
- What is an extraneous root?
- A value that solves the squared (or cubed) equation but not the original one. It appears because raising both sides to a power can add solutions.
- Why convert a quadratic to vertex form?
- Vertex form a(x − h)² + k shows the turning point (h, k) directly, which makes graphing and optimisation problems easier.
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