Q.E.D. — quod erat demonstrandum · every step shown, every result verifiedJournal · ISSN pending · Crossref DOI member
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Calculators

113 tools live, each on its own page with its own URL. Every result comes with steps computed from your inputs — identify, formula, substitution, evaluation — and validity checks that refuse bad inputs instead of silently returning nonsense.

Algebra13 tools

Quadratic Equation Solver

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Roots of ax²+bx+c=0 — real, repeated or complex — via the discriminant.

Linear Equation Solver

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Solve ax + b = 0 for x with the rearrangement shown step by step.

Slope Calculator

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Find the slope m between two points from the rise-over-run formula.

Distance Between Two Points

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Compute the straight-line distance between two points in the plane.

Percentage Calculator

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Find p percent of a number n directly.

Percentage Change Calculator

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Percentage increase or decrease from an old value to a new value.

Exponent Calculator

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Raise a base to any real power.

Logarithm Calculator

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Compute log base b of x via the change-of-base identity.

Nth Root Calculator

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Take the nth root of a positive number.

Arithmetic Sequence Nth Term

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The nth term of an arithmetic sequence from first term and common difference.

Geometric Sequence Nth Term

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The nth term of a geometric sequence from first term and common ratio.

Arithmetic Series Sum

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Sum of the first n terms of an arithmetic sequence.

Geometric Series Sum

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Sum of the first n terms of a geometric sequence.

Geometry19 tools

Circle Area

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Area of a circle from its radius.

Circle Circumference

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Perimeter of a circle from its radius.

Triangle Area (Base × Height)

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Area of any triangle from base and perpendicular height.

Heron's Formula Triangle Area

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Area of a triangle from its three sides, via the semi-perimeter.

Rectangle Area

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Area of a rectangle from length and width.

Rectangle Perimeter

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Perimeter of a rectangle from length and width.

Trapezoid Area

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Area of a trapezium from the two parallel sides and the height.

Parallelogram Area

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Area of a parallelogram from base and height.

Ellipse Area

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Area of an ellipse from its semi-major and semi-minor axes.

Circle Sector Area

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Area of a circular sector from radius and central angle in degrees.

Arc Length

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Length of a circular arc from radius and central angle in degrees.

Sphere Volume

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Volume of a sphere from its radius.

Sphere Surface Area

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Surface area of a sphere from its radius.

Cylinder Volume

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Volume of a right circular cylinder.

Cylinder Surface Area

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Total surface area of a closed cylinder.

Cone Volume

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Volume of a right circular cone.

Cube Volume

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Volume of a cube from its edge length.

Cuboid Volume

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Volume of a rectangular box from its three dimensions.

Pyramid Volume

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Volume of any pyramid from base area and height.

Trigonometry9 tools

Sine Calculator (Degrees)

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Sine of an angle given in degrees.

Cosine Calculator (Degrees)

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Cosine of an angle given in degrees.

Tangent Calculator (Degrees)

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Tangent of an angle given in degrees.

Pythagorean Hypotenuse

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Hypotenuse of a right triangle from the two legs.

Pythagorean Missing Leg

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One leg of a right triangle from the hypotenuse and the other leg.

Law of Cosines — Third Side

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Third side of a triangle from two sides and the included angle.

Triangle Area (Two Sides & Angle)

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Area from two sides and the included angle (SAS).

Degrees to Radians

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Convert an angle from degrees to radians.

Radians to Degrees

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Convert an angle from radians to degrees.

Statistics11 tools

Z-Score Calculator

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How many standard deviations a value lies from the mean.

Combination Calculator (nCr)

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Number of ways to choose r items from n when order does not matter.

Permutation Calculator (nPr)

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Number of ordered arrangements of r items chosen from n.

Coefficient of Variation

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Relative spread of data: standard deviation as a percentage of the mean.

Mean (Average) Calculator

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Arithmetic mean of a data set with the sum and count shown.

Median Calculator

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Middle value of a sorted data set, with the sorting shown.

Sum Calculator

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Total of a list of numbers.

Range Calculator

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Spread of a data set: maximum minus minimum.

Population Variance Calculator

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Average squared deviation from the mean.

Population Standard Deviation

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Square root of the population variance — the typical deviation from the mean.

Sample Standard Deviation

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Standard deviation with Bessel's n−1 correction for samples.

Calculus6 tools

Power Rule Derivative at a Point

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Evaluate d/dx (a·xⁿ) at a chosen point using the power rule.

Definite Integral of xⁿ

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Evaluate the integral of xⁿ from a to b with the antiderivative shown.

Average Rate of Change

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Mean slope of a function between two of its points.

Exponential Growth

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Population or quantity after time t under continuous growth rate k.

Exponential Decay

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Remaining quantity after time t under continuous decay rate k.

Half-Life Remaining Amount

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Amount remaining after time t given the substance's half-life.

Financial11 tools

Simple Interest

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Interest earned on a principal at a flat annual rate.

Compound Interest Amount

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Final amount with interest compounded n times per year.

Loan EMI Calculator

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Fixed monthly instalment for a loan at a given annual rate and tenure in months.

Return on Investment (ROI)

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Percentage gain or loss on the money invested.

CAGR Calculator

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Compound annual growth rate between a starting and ending value.

Future Value of an Annuity

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Value of equal periodic payments accumulated with compound interest.

Present Value

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Today's worth of a future amount discounted at a given annual rate.

Discount Price

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Final price after a percentage discount.

Markup Price

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Selling price after adding a percentage markup to cost.

VAT / GST Inclusive Price

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Price including value-added tax at a given rate.

Break-Even Point (Units)

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Units to sell so total revenue covers fixed and variable costs.

Fluid Mechanics16 tools

Reynolds Number

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Re = ρvD/μ with laminar / transitional / turbulent classification.

Bernoulli Equation

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Solve for downstream pressure P₂ with each term itemised.

Hagen–Poiseuille Flow

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Laminar pipe flow rate Q with a built-in Reynolds validity check.

Dynamic Pressure

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Kinetic energy per unit volume of a moving fluid — the ½ρv² term of Bernoulli.

Hydrostatic Pressure

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Gauge pressure at a depth h in a fluid at rest.

Buoyant Force (Archimedes)

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Upward force on a body equal to the weight of displaced fluid.

Continuity — Downstream Velocity

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Velocity after a change in pipe cross-section, from A₁v₁ = A₂v₂.

Volumetric Flow Rate

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Flow rate through a cross-section from area and mean velocity.

Kinematic Viscosity

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Momentum diffusivity ν from dynamic viscosity and density.

Mach Number

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Ratio of flow speed to the local speed of sound.

Froude Number

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Ratio of inertial to gravitational forces — governs open-channel flow.

Weber Number

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Ratio of inertial to surface-tension forces — droplets, sprays, bubbles.

Stokes Settling Velocity

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Terminal velocity of a small sphere sinking in viscous fluid (creeping flow).

Capillary Rise

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Height a liquid climbs in a narrow tube from surface tension.

Drag Force

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Aerodynamic drag on a body from the drag equation.

Darcy–Weisbach Head Loss

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Friction head loss in a pipe from the friction factor.

Physics12 tools

Force (Newton's Second Law)

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Net force from mass and acceleration.

Kinetic Energy

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Energy of motion from mass and speed.

Gravitational Potential Energy

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Stored energy of a mass raised to height h.

Momentum

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Linear momentum from mass and velocity.

Work Done

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Work by a constant force along its direction of motion.

Power

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Rate of doing work.

Ohm's Law — Voltage

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Voltage across a resistor from current and resistance.

Electrical Power

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Power dissipated from voltage and current.

Density

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Mass per unit volume.

Speed

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Average speed from distance and time.

Acceleration

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Uniform acceleration from a change in velocity over time.

Gravitational Force

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Newton's law of universal gravitation between two masses.

Sequences & Numbers5 tools

Factorial Calculator

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n! — the product of all positive integers up to n.

Fibonacci Nth Term (Binet)

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The nth Fibonacci number from Binet's closed-form formula.

Sum of First n Integers

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Gauss's formula for 1 + 2 + ⋯ + n.

Sum of First n Squares

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Closed form for 1² + 2² + ⋯ + n².

Sum of First n Cubes

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Closed form for 1³ + 2³ + ⋯ + n³ — the square of the triangular number.

Conversions11 tools

Celsius to Fahrenheit

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Convert a temperature from °C to °F.

Fahrenheit to Celsius

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Convert a temperature from °F to °C.

Kilometres to Miles

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Convert a distance from km to miles.

Miles to Kilometres

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Convert a distance from miles to km.

Kilograms to Pounds

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Convert a mass from kg to lb.

Pounds to Kilograms

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Convert a mass from lb to kg.

Metres per Second to km/h

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Convert a speed from m/s to km/h.

Litres to US Gallons

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Convert a volume from litres to US gallons.

Inches to Centimetres

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Convert a length from inches to cm.

PSI to Pascal

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Convert a pressure from psi to pascals.

Bar to Atmospheres

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Convert a pressure from bar to standard atmospheres.