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.
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Roots of ax²+bx+c=0 — real, repeated or complex — via the discriminant.
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Solve ax + b = 0 for x with the rearrangement shown step by step.
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Find the slope m between two points from the rise-over-run formula.
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Compute the straight-line distance between two points in the plane.
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Find p percent of a number n directly.
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Percentage increase or decrease from an old value to a new value.
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Raise a base to any real power.
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Compute log base b of x via the change-of-base identity.
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Take the nth root of a positive number.
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The nth term of an arithmetic sequence from first term and common difference.
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The nth term of a geometric sequence from first term and common ratio.
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Sum of the first n terms of an arithmetic sequence.
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Sum of the first n terms of a geometric sequence.
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Area of a circle from its radius.
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Perimeter of a circle from its radius.
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Area of any triangle from base and perpendicular height.
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Area of a triangle from its three sides, via the semi-perimeter.
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Area of a rectangle from length and width.
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Perimeter of a rectangle from length and width.
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Area of a trapezium from the two parallel sides and the height.
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Area of a parallelogram from base and height.
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Area of an ellipse from its semi-major and semi-minor axes.
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Area of a circular sector from radius and central angle in degrees.
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Length of a circular arc from radius and central angle in degrees.
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Volume of a sphere from its radius.
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Surface area of a sphere from its radius.
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Volume of a right circular cylinder.
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Total surface area of a closed cylinder.
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Volume of a right circular cone.
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Volume of a cube from its edge length.
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Volume of a rectangular box from its three dimensions.
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Volume of any pyramid from base area and height.
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Sine of an angle given in degrees.
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Cosine of an angle given in degrees.
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Tangent of an angle given in degrees.
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Hypotenuse of a right triangle from the two legs.
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One leg of a right triangle from the hypotenuse and the other leg.
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Third side of a triangle from two sides and the included angle.
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Area from two sides and the included angle (SAS).
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Convert an angle from degrees to radians.
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Convert an angle from radians to degrees.
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How many standard deviations a value lies from the mean.
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Number of ways to choose r items from n when order does not matter.
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Number of ordered arrangements of r items chosen from n.
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Relative spread of data: standard deviation as a percentage of the mean.
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Arithmetic mean of a data set with the sum and count shown.
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Middle value of a sorted data set, with the sorting shown.
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Total of a list of numbers.
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Spread of a data set: maximum minus minimum.
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Average squared deviation from the mean.
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Square root of the population variance — the typical deviation from the mean.
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Standard deviation with Bessel's n−1 correction for samples.
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Evaluate d/dx (a·xⁿ) at a chosen point using the power rule.
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Evaluate the integral of xⁿ from a to b with the antiderivative shown.
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Mean slope of a function between two of its points.
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Population or quantity after time t under continuous growth rate k.
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Remaining quantity after time t under continuous decay rate k.
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Amount remaining after time t given the substance's half-life.
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Interest earned on a principal at a flat annual rate.
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Final amount with interest compounded n times per year.
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Fixed monthly instalment for a loan at a given annual rate and tenure in months.
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Percentage gain or loss on the money invested.
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Compound annual growth rate between a starting and ending value.
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Value of equal periodic payments accumulated with compound interest.
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Today's worth of a future amount discounted at a given annual rate.
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Final price after a percentage discount.
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Selling price after adding a percentage markup to cost.
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Price including value-added tax at a given rate.
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Units to sell so total revenue covers fixed and variable costs.
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Re = ρvD/μ with laminar / transitional / turbulent classification.
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Solve for downstream pressure P₂ with each term itemised.
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Laminar pipe flow rate Q with a built-in Reynolds validity check.
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Kinetic energy per unit volume of a moving fluid — the ½ρv² term of Bernoulli.
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Gauge pressure at a depth h in a fluid at rest.
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Upward force on a body equal to the weight of displaced fluid.
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Velocity after a change in pipe cross-section, from A₁v₁ = A₂v₂.
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Flow rate through a cross-section from area and mean velocity.
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Momentum diffusivity ν from dynamic viscosity and density.
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Ratio of flow speed to the local speed of sound.
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Ratio of inertial to gravitational forces — governs open-channel flow.
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Ratio of inertial to surface-tension forces — droplets, sprays, bubbles.
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Terminal velocity of a small sphere sinking in viscous fluid (creeping flow).
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Height a liquid climbs in a narrow tube from surface tension.
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Aerodynamic drag on a body from the drag equation.
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Friction head loss in a pipe from the friction factor.
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Net force from mass and acceleration.
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Energy of motion from mass and speed.
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Stored energy of a mass raised to height h.
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Linear momentum from mass and velocity.
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Work by a constant force along its direction of motion.
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Rate of doing work.
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Voltage across a resistor from current and resistance.
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Power dissipated from voltage and current.
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Mass per unit volume.
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Average speed from distance and time.
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Uniform acceleration from a change in velocity over time.
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Newton's law of universal gravitation between two masses.
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Convert a temperature from °C to °F.
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Convert a temperature from °F to °C.
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Convert a distance from km to miles.
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Convert a distance from miles to km.
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Convert a mass from kg to lb.
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Convert a mass from lb to kg.
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Convert a speed from m/s to km/h.
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Convert a volume from litres to US gallons.
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Convert a length from inches to cm.
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Convert a pressure from psi to pascals.
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Convert a pressure from bar to standard atmospheres.