Science calculators
The working behind physics and chemistry homework — solve a named law for any variable, and see which formula was used.
- Trigonometry CalculatorSine, cosine, tangent and their reciprocals for any angle in degrees, radians or gradians — or work back to the angle with arcsin, arccos and arctan.
- Triangle CalculatorSolve any triangle from three known parts — SAS, SSS, ASA, AAS or SSA. Returns every side and angle, the area, the perimeter, and both ambiguous answers.
- Significant Figures CalculatorCount the significant figures in any number, or round to a set number of them, with every rule shown — leading, trailing and embedded zeros included.
- Scientific Notation CalculatorWrite a number in standard form, or multiply, divide, add and subtract in scientific notation — with the significant-figure rule for each shown in full.
- Ideal Gas Law CalculatorEnter any three of pressure, volume, moles and temperature and get the fourth from PV = nRT, in atm, kPa, bar, mmHg, psi and K, °C or °F.
- Molarity CalculatorWork out molarity from a mass, the mass to weigh out for a target concentration, the volume to make up to, or a dilution using M₁V₁ = M₂V₂.
- Kinematics CalculatorSolve for displacement, final velocity, acceleration or time with the SUVAT equations, with every step shown and the motion plotted against time.
- Vector CalculatorDot and cross product, angle between two vectors, magnitude, unit vector, projection, addition and subtraction, in 2D or 3D, with the working shown.
- Matrix CalculatorDeterminant, inverse, transpose, product, sum or difference of a 2 x 2 or 3 x 3 matrix, with the cofactor expansion and the adjugate written out.
- Linear Regression CalculatorFit a least-squares line to your x and y data, predict y at any x, and see the slope, intercept, r, R² and standard error worked out step by step.
Solve a named law for whichever variable is missing
A physical law is a relationship between quantities, not a one way formula. The ideal gas law relates pressure, volume, moles and temperature, and given any three the fourth follows. The same is true of the kinematic equations, of molarity and dilution, and of the trigonometric relationships in a triangle. Each page here takes the knowns you have rather than the ones a textbook happened to list first, and names the rearrangement it used.
That matters for checking work as much as for producing it. Seeing which form of a law was applied, and with what substitution, is what makes an answer verifiable rather than merely plausible.
Precision that survives the arithmetic
Significant figures are not decoration; they carry a claim about how well something was measured. Multiplication and division keep the fewest significant figures among the inputs, while addition and subtraction keep the fewest decimal places — different rules, applied at different stages, and a calculation mixing both has to apply each where it belongs. A result quoted to more figures than the measurements support is a false claim about precision.
Scientific notation exists for the same reason. Writing 6.02 times 10 to the 23 states three significant figures unambiguously, where 602000000000000000000000 states nothing at all about how many of those digits were measured rather than assumed.
Frequently asked questions
Which value of R should I use in PV equals nRT?
It depends entirely on the units of the other quantities, and using a mismatched R is the most common error in gas law problems. In SI units R is 8.314462618 joules per mole per kelvin, exact by definition since the 2019 redefinition. Working in litres and atmospheres, R is 0.082057 litre atmospheres per mole per kelvin. The value is the same physical constant; only the units differ. Temperature must always be absolute, in kelvin, never in celsius.
Why does my triangle sometimes have two valid answers?
That is the ambiguous case, and it arises when you know two sides and an angle that is not between them. The known angle can be satisfied by two different triangles — one acute and one obtuse — because the sine of an angle equals the sine of its supplement. Depending on the numbers there may be two solutions, exactly one, or none at all if the side is too short to reach. A solver that reports only one answer is hiding the ambiguity rather than resolving it.
What is the difference between significant figures in multiplication and addition?
Multiplication and division keep the smallest number of significant figures found among the inputs: 2.5 times 3.42 gives 8.6, because 2.5 has only two. Addition and subtraction keep the smallest number of decimal places instead: 2.5 plus 3.42 gives 5.9, because 2.5 is known only to one decimal. The rules differ because the two operations propagate uncertainty differently, and a calculation using both has to apply each at the right step.
When should I work in radians rather than degrees?
Radians are the natural unit whenever calculus is involved, because the derivative of sine equals cosine only when the angle is in radians. Degrees are more convenient for geometry, surveying and navigation, where angles are read from instruments. One full turn is 360 degrees or 2 pi radians. Most programming languages take radians by default, which is a frequent source of wrong answers when degrees were intended.