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Every formula, live.

100 formulas from school and first-year university maths. Type your numbers and any formula solves for any of its letters, showing every step. Drag the sliders and watch the graph change.

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Try it: quadratic formula

x=−b±b2−4ac2a
−8−6−4−22468−8−6−4−22468vertex

Drag a, b and c. The roots and the vertex follow.

  • Vertex (1, −8); axis of symmetry x = 1
  • D = 64 > 0: two real roots, x = −1 and x = 3
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Algebra Quadratics, the binomial theorem, logarithms, exponents, growth and decay. 14 formulas Geometry Pythagoras, areas of every common shape, circles and sectors, polygons, volumes and surface areas. 22 formulas Coordinate geometry Distance, midpoint and slope between points; equations of lines and circles; perpendicular lines. 8 formulas Trigonometry SOH CAH TOA, the laws of sines and cosines, identities, radians and sine waves. 9 formulas Sequences and series Arithmetic and geometric sequences, their sums, sums to infinity, and the classic sums of integers and squares. 7 formulas Probability and statistics Mean, standard deviation, z-scores, the normal and binomial distributions, counting, probability rules and Bayes. 13 formulas Finance maths Simple and compound interest, loan repayments, present value, annuities and the rule of 72. 9 formulas Calculus basics Derivative rules, tangent lines, definite integrals, area under a curve and average value. 12 formulas Motion (kinematics) Speed, the constant-acceleration (SUVAT) equations and projectile range. 6 formulas

Formula of the week

Arithmetic series (sum)

Sn=n2(2a1+(n−1)d)

Adds up the first n terms of an arithmetic sequence in one step.

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Every answer is tested before it is published

Each calculator is run against at least five known results, including the awkward cases: negative discriminants, division by zero, degrees versus radians, impossible triangles. Every answer is then fed back in to recover the original inputs. Every worked example on this site is recomputed when the site is built, and the build stops if the text and the arithmetic disagree.

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Test cases
822
Round trips
1226
Worked examples recomputed
100