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The math section covers arithmetic and algebra through geometry, trigonometry and sequences: percentages, fractions, ratios, quadratic equations, logarithms, factors and primes, areas and volumes, right triangles and trigonometry functions. Each calculator shows the formula, names the variables, and works through a complete example with real numbers so you can follow the arithmetic. Most support reverse mode for solving the missing value. The underlying definitions follow standard textbook conventions, and the worked examples double as checks: if you already know the answer a formula should give, enter the numbers and confirm the calculator agrees. All computation happens in your browser. The math pages double as study references, with the definitions and conventions written out alongside the calculators so the formulas are not a black box.
Worked scenarios
Illustrative examples. Every figure was calculated with the tools linked at the foot of each scenario, using the formula each tool documents, so the numbers can be reproduced. They are not client results and they are not advice.
A course grades homework at 20%, quizzes 15%, a midterm 25%, a project 20% and the final 20%. Scoring 88, 92, 78 and 85 on the first four gives 67.9 weighted points out of 80. To finish the course on 80 overall the final needs 60.5%. To finish on 85 it needs 85.5%, which is the number worth knowing before the last week of term.
Worked with: Grade Calculator, Percentage Calculator
Fourteen credits in the semester, plus a one-credit seminar: an A in a four-credit course, a B+ in a three-credit course, a B in another three-credit course, a B minus in a four-credit course and an A minus in the seminar. The grade points total 49.4 across 15 credits, so the GPA is 3.29. The four-credit B minus is what holds it below 3.3.
Worked with: GPA Calculator
Worked case studies: academic
Three scenarios, each with the inputs stated and the result computed. Every figure was calculated with the tools linked at the foot of the study, using the formula each tool documents, so it can be reproduced by entering the same values. They are illustrative examples, not client results, and they are not advice.
A student has to approximate the integral of sin(x) between 0 and pi, where the exact answer is 2, and can choose between the trapezoidal rule and Simpson's rule. Both runs use the same number of subintervals.
Inputs: f(x) = sin(x) on the interval 0 to pi. Four subintervals first, then eight.
Result: At four subintervals the trapezoidal rule returns 1.896119, an error of 0.103881, while Simpson's rule returns 2.004560, an error of 0.004560. At eight subintervals the values are 1.974232 and 2.000269.
What it means: At the same node count Simpson's rule lands more than twenty times closer to the answer, so the choice of method buys more here than doubling the work does.
Worked with: Simpson's Rule Calculator, Trapezoidal Rule Calculator
A surveyor measures the three sides of a triangular plot as 13 m, 14 m and 15 m. There is no right angle to work from and no convenient height to measure.
Inputs: Sides a = 13 m, b = 14 m, c = 15 m.
Result: Heron's formula gives an area of 84 square metres and a perimeter of 42 m. The three angles are 53.13, 59.49 and 67.38 degrees.
What it means: An awkward-looking triangle comes out on an exact whole number of square metres, which is the reason Heron's formula earns its place when nothing can be measured from a right angle.
Worked with: Triangle Calculator, Area Calculator
A poll of 1,000 respondents puts one candidate at 47% and the report calls it a lead. The question is whether the sample supports that word.
Inputs: 1,000 respondents, a proportion of 47%, and 95% confidence. Then 500 and 1,500 respondents for comparison.
Result: The standard error is 1.58 percentage points, so the margin is 3.09 points and the interval runs from 43.91% to 50.09%. At 500 respondents the margin widens to 4.37 points, and at 1,500 it narrows to 2.53 points.
What it means: At 1,000 responses the interval crosses 50%, so the poll does not establish a lead, and the extra precision from a bigger sample arrives slowly.
Worked with: Margin of Error Calculator, Confidence Interval Calculator, Sample Size Calculator
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Basic and scientific calculations.
Work out any percentage instantly.
Add, subtract, multiply, and divide fractions.
Mean, variance, and standard deviation for any data set.
Mean, median, and mode for any list of numbers.
Solve any quadratic equation step by step.
Calculate probability for any event.
Trig, logarithms, powers, and more.
Generate random numbers in any range.
Simplify ratios and solve proportions.
Any base raised to any power.
Area of any 2D shape.
Volume of any 3D shape.
Slope, angle, and equation of a line.
Logarithm in any base.
Sides, angles, and area of any triangle.
Find the missing side of a right triangle.
Add, subtract, multiply binary numbers. Convert to decimal.
Full descriptive statistics for any data set.
Compute phi, segment lengths, total, and a live golden rectangle with nested squares and a spiral.
GCF and LCM of any set of numbers.
Break any number into its prime factors.
Least common multiple and greatest common divisor.
Generate Fibonacci numbers up to any term.
Compute n! (factorial) and n!! (double factorial) for non-negative integers. BigInt precision up to 170!.
Convert any number to English words.
sin, cos, tan and inverses in degrees, radians, or gradians.
Convert between z-scores, probabilities, and percentiles.
Compute confidence intervals for a mean (z or t), two means (Welch t), one proportion, or two proportions. Built-in normal & t quantiles, no precomputed tables.
Area, perimeter, and angles of any regular polygon.
Add, subtract, dot product, cross product, magnitude.
Add, multiply, transpose, and find determinants.
Detect arithmetic, geometric, Fibonacci, and quadratic sequences.
Generate truth tables for any Boolean expression.
Properties of parabolas, ellipses, circles, and hyperbolas.
Two- and three-set Venn diagrams with intersection analysis.
Calculate nPr and nCr with factorial-based formulas.
Simplify fractions to lowest terms using GCD.
Kinetic energy, velocity, or mass from any two values.
Newton's second law: F = ma.
Spring force and constant using Hooke's Law (F = kx).
Mass, volume, or density from any two values.
Convert between wavelength, frequency, and photon energy.
Molar mass of any chemical formula.
Balance any chemical equation automatically.
Calculate the area, circumference, diameter, and radius of a circle.
Calculate the mean, median, mode, range, variance, and standard deviation of any data set.
Calculate the p-value from a test statistic (z-score, t-statistic, chi-squared, or F-st...
Perform one-sample, two-sample independent, and paired t-tests.
Probability of exactly k successes in n independent trials.
Solve for the required sample size n, one-sample mean (z or t), one proportion, two-sample mean (effect & power), or two-sample proportion (effect & power).
Convert degrees to radians and radians to degrees instantly. Bidirectional sync with quick-preset reference points.
Calculate the slope of a line through two points using m = (yโ โ yโ)/(xโ โ xโ).
Compute the greatest common divisor (GCD) of any two integers up to one billion using the Euclidean algorithm, with full step-by-step trace.
Generate Fibonacci numbers (or Lucas-like variants) up to 200 terms with BigInt precision.
Check if a number is prime, sieve a range, find the next prime, or factor any integer into primes.
Compute the prime factorization of any positive integer (up to 10ยฒโต with BigInt). Shows the canonical form, divisor count ฯ(n), sum of divisors ฯ(n), and Euler totient ฯ(n), with a full trial-division step trace.
Multiply any two matrices A (mรn) and B (nรp) and see the row ร column dot-product for every cell of C = A ร B.
Compute the volume V = (1/3)ยทฯยทrยฒยทh, slant height l = โ(rยฒ + hยฒ), base area ฯยทrยฒ, lateral area ฯยทrยทl, and total surface area ฯยทrยฒ + ฯยทrยทl of a right circular cone from any positive radius and height, or solve the inverse to recover the radius from a known volume and height, or the height from a known volume and radius.
Compute sphere volume V = (4/3)ยทฯยทrยณ and surface area A = 4ยทฯยทrยฒ from any positive radius, or solve the inverse problem to recover the radius from a known volume or surface area.