Conversion & Math
The arithmetic people do at a desk or on a phone: percentages, fractions, areas, time spans and unit-carrying values. Inputs accept the forms people actually type — 5ft 11in, 3/8, 2 1/4 — rather than requiring a single decimal number.
Conversions, geometry and the percentage arithmetic people get wrong most often.
Percentages & rates
- Percentage Change CalculatorPercentage increase or decrease between two values, with the absolute difference and the multiplier.
- Percentage CalculatorWhat X% of a number is, plus the discounted price, the marked-up price and the remainder.
- Speed & Pace CalculatorAverage speed and running pace from a distance and a time, in both imperial and metric.
- Percent Off CalculatorThe sale price after a discount, after a second discount stacked on it, and after tax — with what you actually saved.
- Ratio CalculatorReduce a ratio to simplest terms, restate it as 1 : n, and solve a proportion for its missing term.
- Percent Error CalculatorPercent error against a known value, with percent difference beside it — they are different questions and get confused constantly.
- Percent DifferencePercent difference between two values, divided by their mean — beside percent change, which divides by one of them and gives a different answer.
Geometry
- Diagonal & Rafter Length CalculatorHypotenuse of a right triangle in feet and inches — brace lengths, rafter runs, and squaring a layout.
- Circle CalculatorArea, circumference and radius of a circle from its diameter — in square feet and square inches.
- Tank & Cylinder Volume CalculatorVolume of a cylinder in cubic feet, US gallons and liters — round tanks, pools, culverts and post holes.
- Slope & Grade CalculatorGrade percentage, angle in degrees, ratio and roof pitch from a rise and a run.
- Cone Volume CalculatorVolume of a cone from its diameter and height, in cubic feet, cubic inches and gallons, with the radius and the base area shown separately.
- Sphere Volume CalculatorVolume and surface area of a sphere from its diameter, in cubic feet, cubic inches and gallons, with the radius shown as its own step.
- Circumference CalculatorCircumference of a circle from its diameter or the other way round, with the radius, the area and the arc of one degree shown alongside.
- Right Triangle CalculatorHypotenuse, area, perimeter and both acute angles of a right triangle from its two legs, with the Pythagorean step shown before the square root.
- Arc Length and Sector Area CalculatorArc length, sector area, chord and sector perimeter from a radius and an angle, with the fraction of the full circle shown as its own step.
- Special Right Triangle CalculatorThe 45-45-90 and 30-60-90 triangles from one known side, with every other side given as an exact multiple rather than a decimal that hides the ratio.
- Semicircle CalculatorArea and perimeter of a half circle from its diameter — and the perimeter is the part people get wrong, because it includes the straight edge.
- Pyramid Volume CalculatorVolume of a rectangular pyramid from its base and height, in cubic feet and cubic yards, with the box of the same base and height shown for comparison.
- Volume CalculatorVolume of a tank, cube, cylinder, sphere, cone, frustum, pyramid, capsule, ellipsoid or pipe — in cubic feet, US gallons and liters.
- Area CalculatorArea of a rectangle, triangle, circle, sector, ellipse, trapezoid, parallelogram or regular polygon — in square feet, square yards, acres and square meters.
- Distance Formula CalculatorDistance between two points in the plane or in space, with the midpoint and the slope, and every step of the square root shown.
- Distance Between CoordinatesGreat-circle distance between two latitude and longitude pairs, in miles, kilometers and nautical miles, with the initial bearing.
- Surface Area CalculatorSurface area of a box, cube, cylinder, sphere, cone, pyramid, capsule or ellipsoid, with the lateral area given separately from the ends.
- Slope CalculatorSlope, intercept, angle and the full line equation from two points, with the perpendicular slope beside it.
- Triangle CalculatorEvery angle, the area, the perimeter and the height of any triangle from its three sides, using the law of cosines.
- Pythagorean Theorem CalculatorSolves a² + b² = c² in either direction — the hypotenuse from two legs, or the missing leg from a leg and the hypotenuse — with the squares shown.
- Midpoint CalculatorThe midpoint of two points, with the distance, the slope and the perpendicular bisector — what a coordinate-geometry question asks about the same pair.
- Dot and Cross ProductDot product, cross product, magnitudes and the angle between two 3-D vectors. The dot returns a number, the cross returns a vector — that is the difficulty.
- Sin Cos Tan CalculatorSine, cosine and tangent of an angle in degrees or radians, with the angle also shown in the other unit and the reciprocal functions.
- Inverse Trig CalculatorArcsine, arccosine and arctangent: the angle whose sine, cosine or tangent is the ratio you have, in degrees and radians.
- Law of Sines CalculatorSolves a triangle from one side and two angles: the third angle, the remaining two sides and the area, using a/sin A = b/sin B.
- Law of Cosines CalculatorSolves a triangle from two sides and the angle between them: the third side, the other two angles and the area, using c² = a² + b² − 2ab·cos C.
Conversion
- Fraction to Decimal CalculatorConverts fractions to decimals and back, to the nearest 16th, 32nd and 64th, with the millimeter equivalent.
- Military Time ConverterA clock time as military time, with the full chart of all twenty-four hours and the two readings people get wrong: midnight and noon.
- Tire Size CalculatorWhat a tire size means in inches, and what changing it does to the rolling diameter and to the speedometer reading.
- Height ConverterConverts height between centimeters, meters and feet-and-inches in either direction. With the centimeters-to-feet chart most people are actually looking for.
- Temperature ConverterConverts between Celsius, Fahrenheit and Kelvin in any direction, with the reference points to sanity-check it.
- Grams to Cups ConverterCups to grams and back for 93 ingredients, and what the same cup weighs depending on how it was filled.
- Density CalculatorDensity from mass and volume, in kilograms per cubic meter, grams per cubic centimeter and pounds per cubic foot, with what floats and what does not.
- Rounding CalculatorA number rounded every way there is — half up, half to even, down, up and truncated — with the ones that disagree shown together.
- Exponent CalculatorA number raised to any power, including negative and fractional ones, with the root it is equivalent to and the answer in scientific notation.
- Logarithm CalculatorA logarithm in any base, with the natural and base-ten values beside it and the change-of-base step shown.
- Half-Life CalculatorHow much of a substance is left after a given time, from its half-life — with the decay constant and the mean lifetime.
- Heat Index CalculatorWhat the temperature feels like at a given humidity, by the National Weather Service regression, with the risk category it falls in.
- Wind Chill CalculatorWhat the cold feels like once wind is taken into account, by the National Weather Service formula, with the frostbite time it implies.
- Dew Point CalculatorDew point from temperature and humidity by the Magnus formula, with what that dew point actually feels like.
- Scientific Notation ConverterA number in scientific, engineering and plain notation at once, with its order of magnitude and significant figures.
- Molarity CalculatorMolarity from mass and volume, the mass needed for a target concentration, and the dilution that gets you there.
- Oven Temperature ConverterAn oven setting in Fahrenheit, Celsius, gas mark and the fan equivalent, with the dial rounding real ovens actually offer.
Fractions
- GCF and LCM CalculatorGreatest common factor and least common multiple of two or three numbers, with the prime factors and the check that ties them together.
- Fraction CalculatorAdd, subtract, multiply or divide fractions and mixed numbers, with an exact reduced answer and every step shown.
- Simplify Fractions CalculatorReduce a fraction to lowest terms, showing the greatest common divisor it was divided by.
- Mixed Numbers CalculatorConvert a mixed number to an improper fraction and back, and add, subtract, multiply or divide two of them.
Algebra
- Quadratic Formula CalculatorBoth roots of ax² + bx + c = 0 from the quadratic formula, with the discriminant that says in advance how many real roots there are.
- Completing the Square CalculatorTurns ax² + bx + c into a(x − h)² + k, giving the vertex, the axis of symmetry and the roots that fall straight out of the completed form.
- Absolute Value CalculatorThe absolute value of a number, and the two solutions an equation of the form |ax + b| = c always has — which is the part a bare magnitude does not answer.
- Difference of Two SquaresFactors a² − b² into (a + b)(a − b), multiplied back out as a check — and the mental shortcut it gives for products either side of a round number.
Time & dates
- Age CalculatorExact age in years, months and days from a birth date, plus the total days lived and the next birthday.
- Hours CalculatorHours worked between two times, less breaks, in decimal payroll hours — with what the federal rounding rules do to the total.
- Date CalculatorWhat date falls a given number of days or weeks from another date, counting calendar days or business days.
- Time CalculatorAdd, subtract, multiply or divide durations in days, hours, minutes and seconds, with the decimal hours payroll and billing want.
- Day CounterHow many days lie between two dates, counted as calendar days and again as working days, with the span in weeks, months and years.
- Minutes to DecimalHours and minutes as the decimal a payroll system wants, with the quarter-hour rounding the FLSA allows and what it costs you over a year.
Statistics
- Z-Score to P-Value CalculatorExact p-value from a z-score, one-tailed or two-tailed, with the percentile the score sits at.
- Grade CalculatorYour weighted course grade from up to eight categories, by percentage or by points, or the score you need on the final to reach the grade you want.
- Confidence Interval CalculatorThe confidence interval around a sample mean, with the margin of error and what the interval does and does not claim.
- Sample Size CalculatorHow many people a survey needs for a given margin of error, with the finite population correction that makes small populations cheaper.
- Probability CalculatorTwo events combined every way — both, either, neither, exactly one — plus the chance of at least one occurrence over many tries.
- Number Sequence CalculatorThe nth term and the running total of an arithmetic or geometric sequence, and whether an infinite geometric one converges.
- Sig Fig CalculatorHow many significant figures a number has and what it rounds to, with the leading, trailing and captive zeros counted by the rules that decide them.
- Correlation CalculatorPearson correlation from the sums a class is given, with r², the slope it implies, and the sample size at which it stops being noise.
- Linear Regression CalculatorThe least-squares line through a set of points, with its slope, intercept, r² and the standard error the prediction carries.
- Binomial CalculatorThe probability of exactly k successes in n independent trials, with the cumulative tails, the mean and the standard deviation.
- Interpolation CalculatorThe value between two known points on a straight line, with the slope it assumes and a warning when the target sits outside them.
- Hypergeometric CalculatorThe probability of drawing exactly k of a kind from a finite population without replacement — the card and lottery case the binomial gets wrong.
- Factorial Calculatorn factorial for n up to 170, with the number of digits, the previous factorial and what the figure counts: the orderings of n distinct things.
Digital
- Pixels to Inches CalculatorPhysical size of a pixel measurement at a given resolution, in inches, centimeters and points — and the resolution is the whole question.
- Download Time CalculatorHow long a file takes at a given connection speed, with the bits-and-bytes factor of eight that makes everyone’s estimate wrong.
Vehicles
- Fuel Consumption ConverterMiles per gallon, liters per 100 km and kilometers per liter from any one of them, with the US and imperial gallons kept apart.
- Horsepower and Torque CalculatorHorsepower from torque and engine speed, with the kilowatt and metric PS figures the same engine is sold under elsewhere.
- Engine Displacement CalculatorEngine capacity from bore, stroke and cylinder count, in cubic centimeters, liters and cubic inches.
Electricity
- Ohm's Law CalculatorVoltage, current, resistance and power from any two of them, with the whole set printed rather than the one you asked for.
- Resistor Colour Code CalculatorResistance and tolerance from the bands on a resistor, with the E-series value it is meant to be.
- Voltage Drop CalculatorVoltage lost along a copper or aluminium run, as volts and as a percentage, against the 3% the NEC recommends for a branch circuit.
- Watts to AmpsWatts to amps and back, with the power factor and the phase that AC needs. A DC answer applied to a 3-phase motor is out by 73%.
- kW and kVA to AmpsCurrent drawn by a load rated in kW or kVA, on any voltage and phase. The unit on the nameplate decides whether power factor enters the sum.
- Volts to WattsVolts alone do not give watts — one more quantity is required. Enter amps, ohms or the wattage and this gives the rest of the set.
- mAh to WhBattery capacity in mAh converted to watt-hours, which is the only figure two batteries at different voltages can be compared on — and the one airlines limit.
- Watts to kWhWatts is a rate and kWh is an amount, so the conversion needs a duration. This gives the energy, the running cost and what the meter will show.
- Joules to WattsA watt is a joule per second, so the conversion is a division by the time. Works either direction, and in kJ, kWh and calories.
- Parallel ResistorsUp to four resistors in parallel or series, with the current each one takes and the power it has to dissipate — which is what decides the rating.
- LED Resistor CalculatorThe series resistor an LED needs, from supply voltage, forward voltage and current — with the power it must dissipate and which standard value to pick.
- dBm to Watts CalculatorConverts dBm to watts and milliwatts, and back — the logarithmic power scale radio, fibre and audio equipment is specified in.
- Decibel CalculatorThe decibel figure for a ratio of two powers or two amplitudes, and the ratio a decibel figure stands for, using 10·log₁₀ and 20·log₁₀.
- Lumens to Lux CalculatorIlluminance in lux from a luminous flux in lumens spread over an area, with the foot-candle equivalent and the area needed for a target level.
- Resonant FrequencyResonant frequency of an LC circuit from inductance and capacitance, with the angular frequency, the period and the capacitance a target frequency needs.
Sport
Physics
- Kinetic Energy CalculatorKinetic energy from mass and speed, with the stopping distance it implies — because the square on the velocity is the part that surprises people.
- Velocity CalculatorFinal velocity from a starting velocity, a constant acceleration and a time, with the distance covered and the average velocity over the interval.
- Momentum CalculatorMomentum from a mass and a velocity, with the kinetic energy that goes with it and the impulse needed to stop the object in a given time.
- Work CalculatorWork done by a force over a distance, with the angle between them, plus the power if it took a given time and the same figure in calories.
- Mass-Energy CalculatorThe rest energy of a mass from E = mc², in joules, kilowatt-hours and kilotons of TNT, using the defined speed of light.
Reference charts
- Inch Fraction to Decimal Chart — 63 rows
- Centimeters to Feet and Inches Chart — 61 rows
- Circle Area and Circumference Chart — 40 rows
- Roof Pitch to Angle and Grade Chart — 24 rows
- Fahrenheit to Celsius Chart — 59 rows
- Z-Score to P-Value Table — 76 rows
- Final Exam Grade Needed, by Current Grade — 29 rows
- Cups to Grams Chart — 60 rows
- Percent Off Chart — 18 rows
- Voltage Drop Chart: 10 AWG Copper at 20 A — 19 rows
- Oven Temperature Chart: °F, °C, Gas, Fan — 16 rows
- Minutes to Decimal Hours Chart — 60 rows
- Watts to Amps Chart — 30 rows
- mAh to Wh Chart — 26 rows
Guides
- How to Use a Protractor — Lining up the vertex, choosing between the two scales — the one to read starts at zero on your baseline — and reading an angle past 180° without inverting it.