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➗ MathFree
Vector magnitude calculator
The vector (3, 4) has a magnitude of 5 and the unit vector (0.6, 0.8): enter the components in 1 to 256 dimensions and get the length, its square and the…
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➗ MathFree
Vector projection calculator
Projecting (3, 4) onto (1, 0) gives a scalar projection of 3, the vector (3, 0) and a perpendicular leftover of (0, 4).
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➗ MathFree
Vieta's formulas calculator
For x² − 3x + 2 the roots add up to 3 and multiply to 2, read straight from the coefficients with Vieta's formulas and without solving the equation.
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🔬 ScienceFree
Angular size calculator
The Sun, 1392000 km across and 149597870.7 km away, spans about half a degree on the sky. Enter any size and distance in the same unit and get the exact angle…
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🔬 ScienceFree
Apoapsis and periapsis calculator
An orbit with a semi-major axis of 7000 km and an eccentricity of 0.05 swings out to 7350 km and in to 6650 km.
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🔬 ScienceFree
Apparent brightness calculator
Double the distance to a star and its apparent brightness falls to a quarter; triple it and it drops to a ninth.
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🔬 ScienceFree
Planet escape velocity calculator
Leaving Earth, with 5.972e24 kg of mass and a 6371000 m radius, takes just over 11 km/s in the ideal case.
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🔬 ScienceFree
Distance modulus calculator
A star of apparent magnitude 10 and absolute magnitude 5 has a distance modulus of 5 and lies 100 parsecs away, or 326.1563777167 light-years.
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🔬 ScienceFree
Geostationary orbit calculator
Around Earth, a geostationary satellite orbits 35786.1067691 km above the equator, at a radius of 42164.2437691 km.
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🔬 ScienceFree
Gravitational force calculator
Earth pulls on a 70 kg person at its surface with 687.421160537 newtons. Enter two masses in kilograms and the distance between their centres in metres to get…
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🔬 ScienceFree
Hubble law calculator
A galaxy receding at 7,000 km/s with a Hubble constant of 70 km/s/Mpc lies 100 megaparsecs away, or 326156377.7 light-years.
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🔬 ScienceFree
Light-year converter
Turn light-years into kilometres, parsecs and astronomical units in one step: one light-year is 9,460,730,472,580.8 km, about three tenths of a parsec.
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🔬 ScienceFree
Orbital energy calculator
See how tightly a satellite is held by its planet: a 1000 kg satellite 6,778,000 m from Earth's centre has a total orbital energy of -29,403,156,980 joules.
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🔬 ScienceFree
Orbital period calculator
Find how long one lap takes around a heavy central body: 149,597,870,700 m from a body of the Sun's mass gives about 365.25 days.
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🔬 ScienceFree
Orbital velocity calculator
Find the speed that keeps a satellite on a circular orbit: 6,778,000 m from the centre of a body with Earth's mass, it must travel at 7,668.527496 m/s.
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🔬 ScienceFree
Stellar parallax calculator
A parallax of 0.1 arcseconds puts a star 10 parsecs away, or 32.61563777 light-years. Enter the angle from a catalogue, a textbook or your own measurement and…
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🔬 ScienceFree
Redshift calculator
A line emitted at 600 and observed at 660 has a redshift z of 0.1, a recession speed of 29979.2458 km/s.
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Roche limit calculator
With densities of 5514 and 3340 kg/m³ and a primary radius of 6371000 m, the rigid Roche limit is 9486901.0016 m and the fluid one 18372610.2884 m.
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🔬 ScienceFree
Synodic period calculator
Work out the wait between matching line-ups of two planets: Earth at 365.25 days and Mars at 686.98 days meet again every 779.906893979 days, the rhythm of Mars…
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🔬 ScienceFree
Rocket equation calculator
Turn exhaust speed and mass ratio into the velocity change a stage can deliver in empty space with no outside forces: 3000 m/s with a mass ratio of…
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🔬 ScienceFree
Weight on other planets calculator
Find your weight on another world from your bathroom-scale reading: 70 kg on Earth becomes 26.39 on Mars, where gravity is 0.377 of Earth's, in the same unit…
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🔬 ScienceFree
Actual yield calculator
A reaction with a theoretical yield of 10 g and a percent yield of 85 should give 8.5 g of product.
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🔬 ScienceFree
Activation energy calculator
Rate constants of 0.0001 at 300 K and 0.0004 at 310 K give reciprocal temperatures of 0.003333333333 and 0.003225806452 and an activation energy of…
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🔬 ScienceFree
Arrhenius pre-exponential factor calculator
A rate constant of 0.001 with an activation energy of 50000 J/mol at 298.15 K gives a pre-exponential factor of 574938.003485542, in the same units as k.
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🔬 ScienceFree
Atom economy calculator
Measure how much of the reactants ends up in the product: hydrating ethene to ethanol, 46.07 g/mol on both sides, scores 100 %.
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🔬 ScienceFree
Atoms to moles of compound calculator
Turn an atom count into moles of compound: 1.806642228 × 10²⁴ atoms grouped three per formula unit, as in water, make exactly 1 mol.
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🔬 ScienceFree
Average atomic mass calculator
Get the weighted average behind a periodic-table value: boron's isotopes at 10.012937 u and 11.009305 u, with abundances 0.199 and 0.801, give 10.811027768 u.
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🔬 ScienceFree
Average kinetic energy of gas calculator
Find how much motion energy a gas molecule carries on average: at 300 K it is 6.2129205 × 10⁻²¹ J, three-halves of Boltzmann's constant times the kelvin…
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🔬 ScienceFree
Avogadro's law calculator
Predict a gas's new volume when only the amount of gas changes: 2 litres holding 1 mol become 6 litres at 3 mol, with temperature and pressure unchanged.
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🔬 ScienceFree
Moles to atoms calculator
Convert both ways with Avogadro's number: 1 mol is 6.02214076 × 10²³ atoms, molecules or ions, and a particle count divided by that number gives moles.
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🔬 ScienceFree
Bomb calorimeter calculator
Turn a bomb calorimeter reading into a molar heat of combustion: a calorimeter constant of 1255 J/K and a rise of 2.45 K for 0.01 mol of sample give −307475…
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🔬 ScienceFree
Bond energy reaction enthalpy calculator
Estimate the heat of a reaction from average bond energies: breaking four C-H and two O=O bonds and forming two C=O and four O-H bonds gives −808 kJ/mol, an…
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🔬 ScienceFree
Boyle's law calculator
Find the new pressure of a gas squeezed or expanded at constant temperature: 2 atm in 3 litres becomes 4 atm when the volume drops to 1.5 litres.
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Boyle's law final volume calculator
Find the volume a gas fills after an isothermal pressure change: 3 litres at 2 atm shrink to 1 litre at 6 atm, because pressure times volume stays the same.
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Buffer capacity calculator
Measure how strongly a buffer resists pH change: 0.1 mol/L of weak acid and 0.1 mol/L of its conjugate base give a capacity of 0.11512925465 mol/(L·pH), the…
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🔬 ScienceFree
Buffer pOH calculator
Get the pOH of a weak-base buffer from pKb and two concentrations: with pKb 4.75 and 0.1 mol/L each of base and conjugate acid, the pOH is 4.75 and the pH at 25…
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🔬 ScienceFree
C1V1 = C2V2 calculator
Solve a dilution for whichever value is missing: 50 mL of a 2 mol/L stock diluted to 0.5 mol/L makes 200 mL, a fourfold dilution.
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🔬 ScienceFree
Calorimeter constant calculator
Calibrate your calorimeter: 1250 J of known heat that warms it by 2.5 °C gives a constant of 500 J/°C, ready to turn later temperature changes into energy.
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🔬 ScienceFree
Calorimetry heat released calculator
Work out the heat a sample takes in or gives off: 1 kg of water with a specific heat of 4184 J/(kg·K), warmed by 1 K, absorbs 4184 J.
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🔬 ScienceFree
Catalyst rate enhancement calculator
See how much a catalyst speeds up a reaction: cutting the activation energy from 75000 to 50000 J/mol at 298.15 K makes it roughly 24 thousand times faster.
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🔬 ScienceFree
Cell potential from Gibbs free energy
Turn a standard Gibbs energy change into a cell voltage: −212300 J/mol with 2 electrons transferred gives 1.100167224278 V, the Daniell zinc-copper cell.
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🔬 ScienceFree
Charles law final temperature calculator
Work out how hot a gas must be to reach a new volume at constant pressure: going from 2 to 4 litres at 273.15 K gives 546.3 K.
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Clausius–Clapeyron calculator
Find the temperature where a liquid reaches a target vapor pressure: from water at 101325 Pa and 373.15 K, with 40650 J/mol, you get the temperature for 2339…
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🔬 ScienceFree
Colligative particle concentration calculator
Turn a formal molarity into the number of dissolved particles that actually counts: 0.1 mol/L of a salt with a van't Hoff factor of 2 gives 0.2 mol/L of…
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🔬 ScienceFree
Collision theory rate calculator
Build a rate constant from how often molecules collide, how often they line up and how many clear the energy barrier: with Z of 10¹¹, a steric factor of 0.5 and…
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🔬 ScienceFree
Combined equilibrium constant calculator
Get the overall equilibrium constant of a reaction built from steps: a step with K of 2.5 plus a reversed step with K of 0.4 gives 6.25, because constants…
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🔬 ScienceFree
Combined gas law final pressure calculator
Work out the new pressure of a gas whose volume and temperature change together: 1 atm, 2 litres and 300 K squeezed to 1 litre at 600 K gives 4 atm.
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🔬 ScienceFree
Combustion analysis calculator
Turn the products of a combustion train into an empirical formula: 3.52 g of CO2 and 1.44 g of H2O point to CH2.
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Common ion effect solubility calculator
Find how far a common ion pushes down a salt's solubility: with a Ksp of 1.8 × 10⁻¹⁰ and 0.1 mol/L of a shared ion, the molar solubility drops to 1.8 × 10⁻⁹…
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🔬 ScienceFree
Gas compressibility factor calculator
Measure how far a real gas strays from ideal behaviour: at 101325 Pa, 273.15 K and 0.022414 m³/mol, Z comes out practically equal to 1.
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Concentration after evaporation calculator
See how strong a solution gets when solvent boils or dries off: evaporating 40 mL from 100 mL of a 2 M solution leaves 60 mL at 3.33 M, a factor of 1.67.
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🔬 ScienceFree
Conjugate base to acid ratio calculator
Know the base-to-acid mix a buffer needs at a given pH: at pH 4.76 with a pKa of 4.76 the ratio is exactly 1, so both forms are equal.
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Faraday corrosion rate calculator
Convert a corrosion current into thickness lost per year: 1 µA/cm² on iron, at 55.845 g/mol, 7.87 g/cm³ and two electrons, eats away a little over 0.01 mm a…
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🔬 ScienceFree
Van der Waals critical constants calculator
Turn the two van der Waals constants of a gas into its critical point: a nitrogen-like gas with a of 1.382 and b of 0.0387 L/mol has a critical volume of 0.1161…
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🔬 ScienceFree
Partial pressures from mole amounts
Share out a mixture's total pressure from how many moles of each gas it holds: 2, 1 and 1 mol at a total of 1 atm give partial pressures of 0.5, 0.25 and 0.25…
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🔬 ScienceFree
Gas mole fraction from partial pressure
Find what share of a gas mixture one component makes up: oxygen at 0.21 atm in air at 1 atm has a mole fraction of 0.21, or 21 %.
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Degree of dissociation calculator
See how much of a reactant has split apart by equilibrium: starting at 0.1 mol/L and ending with 0.02 mol/L undissociated gives a degree of dissociation of 0.8…
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🔬 ScienceFree
Density calculator
Give any two of mass, volume and density and the calculator works out the third: 10 kg in 2 m³ is a density of 5 kg/m³.
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🔬 ScienceFree
Dilution calculator
Fill in three of the four dilution values and get the missing one: 10 mL of a 2 M stock diluted to 0.5 M makes 40 mL of solution.
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Dilution factor calculator
Turn two volumes into a dilution factor and the share of stock left in the mix: 1 mL of solute in a 10 mL total is a tenfold dilution with a solute fraction of…
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