Twelve kinds of physics problem with every constant named as defined, measured or conventional, results printed to the figures those constants justify, and an independent check on each answer.
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Molar mass, equation balancing, pH and the gas laws on all 118 elements of the IUPAC 2021 table, with every interval mass and every approximation named.
Exact arithmetic on rationals, with both evaluation conventions named and the precedence table the parser runs on printed on the page.
Plot functions with a real expression parser, poles drawn as gaps, and roots, turning points and integrals found by bracketing with the check printed.
You need the weight of a 70 kg person, and you want to know how many of the digits you are being shown are real.
Force mode
mass 70 kg · acceleration 2 m/s²
Results
F = ma = 140 N Weight = mg₀ = 686.4655 N g₀ = 9.80665 m/s², exact by convention (3rd CGPM 1901)
Standard gravity is exactly 9.80665 m/s² by definition, so 686.4655 is exact to every digit shown; writing 9.81 instead gives 686.7000, which is wrong in the fourth significant figure. The page also says that g₀ is a CONVENTION rather than a measurement: real surface gravity runs from about 9.7639 at the equator to 9.8337 at the poles, a spread twenty times larger than the error it just avoided.
Twelve kinds of physics problem from one page: force, energy, kinematics, power, momentum and collisions, gravitation, projectile motion, Ohm's law, waves, the pendulum, heat and relativity. Every constant is named as defined, measured or conventional, and every answer is printed only to the number of significant figures its constants can support.
There are three kinds of number in physics and mixing them is how a calculator ends up lying by omission. A DEFINED constant is exact by an act of definition and has no last digit: the speed of light is 299,792,458 m/s because the metre is defined from it, and the Planck, Boltzmann, Avogadro and elementary-charge constants have been exact since the 2019 revision of the SI. A MEASURED constant carries an uncertainty: the Newtonian constant of gravitation is 6.67430(15) x 10^-11, a relative standard uncertainty of 2.2 x 10^-5, so only about five significant figures of any gravitational force are real however many the arithmetic produces. A CONVENTIONAL value is fixed by agreement and true of nothing in particular: standard gravity is exactly 9.80665 m/s^2 by the third CGPM of 1901, and it is not the acceleration anywhere on Earth, where real surface gravity runs from about 9.7639 at the equator to 9.8337 at the poles. This tool prints the whole table with each constant labelled, uses the defined value everywhere, and reports how many figures of each result are justified. Several answers also carry a check computed from a different equation: kinematics is checked against v^2 = u^2 + 2as, projectile motion against the trajectory equation, momentum against the conservation of both momentum and kinetic energy, and Ohm's law against the three forms of the power equation.
Twelve standard problems with the working printed and an independent check on each answer.
A textbook using 9.8 or 9.81 will differ in the third or fourth figure, and this page says exactly why.
The constants panel says how many figures of an answer are real, which for anything involving G is about five.
Force, power, heat and Ohm's law with the units and conversions stated rather than assumed.
The Lorentz factor and rest energy for any speed below c, with the classical limit shown as a check.
Because 9.80665 m/s² is the exact value of standard gravity fixed by the third General Conference on Weights and Measures in 1901. Writing 9.81 introduces a relative error of 3.4 x 10^-4, which is larger than the last digit of anything this page prints. It is worth knowing that neither number is the acceleration at any particular place: real surface gravity varies by 0.7 percent with latitude.
Because G is measured rather than defined, with a relative standard uncertainty of 2.2 x 10^-5. Printing ten figures of a force computed from it would be claiming precision that was never in the input. The page prints what is justified and says how many that is.
A second, independent equation applied to the answer. Kinematics is checked against v² = u² + 2as, which is a different relation from v = u + at; projectile motion is checked by substituting the range into the trajectory equation; a collision is checked against the conservation of momentum and of kinetic energy. None of those needs anything external.
No, and the page says so. For a thrown ball that is a few percent; for anything light or fast it is most of the answer.
The Planck constant, the elementary charge, the Boltzmann constant and the Avogadro constant became exact, which made the kilogram, ampere, kelvin and mole definitions depend on them. The vacuum permeability went the other way: it was exactly 4π x 10⁻⁷ and is now a measured quantity. The constants table marks all of that.
Because reading it as 70 would be a guess about what was meant. Values are read against a stated grammar and anything outside it is refused by name, where parseFloat would silently stop at the space and return 70.
Every calculation runs locally in your browser. Your numbers and expressions are not transmitted or stored.