How to Use Physical Constants Without Losing Marks
Physical constants are the fixed numbers that turn a proportionality into an equation. The speed of light, the gravitational constant, the elementary charge, Planck's constant — each anchors a piece of physics to reality. Students rarely get the concepts wrong here; they lose marks on the mechanics of using constants: a misplaced power of ten, the wrong units, or a value memorized imperfectly.
This guide covers how to work with constants cleanly: which handful are worth memorizing, how to manage scientific notation without slips, why units matter as much as the number, and how to think about uncertainty. A good constants reference removes the arithmetic risk, but knowing the pitfalls is what keeps your setups correct.
Which constants to memorize
You do not need to memorize precise values. Memorize the everyday constant — standard gravity, g ≈ 9.81 m/s² — because you use it constantly, and know the rough magnitude of the others so you can sanity-check a value you look up. Recognising that the speed of light is about 3 × 10⁸ m/s or that the elementary charge is around 1.6 × 10⁻¹⁹ C lets you catch a mistyped value instantly.
- Standard gravity: g ≈ 9.81 m/s².
- Speed of light: c ≈ 3.00 × 10⁸ m/s.
- Elementary charge: e ≈ 1.60 × 10⁻¹⁹ C.
- Gravitational constant: G ≈ 6.67 × 10⁻¹¹ N·m²/kg².
- Avogadro constant: Nₐ ≈ 6.02 × 10²³ mol⁻¹.
Powers of ten are where marks vanish
Most constants are written in scientific notation for good reason — they span from 10⁻³⁴ (Planck's constant) to 10²³ (Avogadro's number). The commonest error is mishandling the exponent when entering a value into a calculator or combining constants. Always enter the exponent with your calculator's dedicated notation key rather than typing '× 10 ^', which invites bracket mistakes.
When multiplying or dividing constants, handle the mantissas and the powers of ten separately, then recombine. Keeping the exponent arithmetic explicit makes an off-by-a-few error obvious instead of silent.
Units are half of the constant
A constant's value is meaningless without its units, and the units tell you where it belongs. The gravitational constant carries units of N·m²/kg² precisely so that, when combined with masses in kilograms and a distance in metres, Newton's law of gravitation delivers a force in newtons. If your other quantities are not in SI base units, the constant's carefully matched units no longer cancel correctly.
This makes units a built-in check. Carry them through any calculation involving a constant; if they do not collapse to the expected unit for your answer, either a quantity is in the wrong unit or the constant was applied incorrectly.
Uncertainty and significant figures
Some constants are exact by definition — the speed of light is now a defined value — while others, like the gravitational constant, carry measurement uncertainty. For exam work you rarely need the uncertainty itself, but it dictates how many significant figures are meaningful. Quoting an answer to eight figures when your constant is known to four is false precision.
A sound rule of thumb: your answer should carry no more significant figures than the least precise value that went into it. Round at the end, not partway through, to avoid compounding rounding errors.
Look it up, then check it
Professionals look constants up rather than trusting memory for precise values, and you should too. A searchable constants reference — PhysRef groups them into universal, electromagnetic, atomic, thermodynamic, Earth, and practical categories — gives the value, symbol, and units together, so you copy all three and match them to your equation. Then apply your magnitude check: does the value you pasted have roughly the exponent you expected? That two-second habit catches the errors that cost marks.
A worked example with a constant
Take the electrostatic force between two charges of one microcoulomb each, held a centimetre apart. Coulomb's law needs the Coulomb constant, k ≈ 8.99 × 10⁹ N·m²/C². Before anything else, convert the given quantities to SI base units: one microcoulomb is 1 × 10⁻⁶ C, and one centimetre is 0.01 m. Skipping that step is the single most common way this calculation goes wrong.
Now assemble the pieces. The force is k times the product of the charges divided by the distance squared: 8.99 × 10⁹, times (10⁻⁶)², divided by (0.01)². Handling the powers of ten deliberately — the numerator carries 10⁹ and 10⁻¹², the denominator 10⁻⁴ — keeps the exponent arithmetic honest and yields a force of roughly 90 newtons. Finally, check the units: the constant's N·m²/C² combined with charges in coulombs squared and a distance in metres squared leaves newtons, exactly as a force should. The value was looked up, the units carried through, and the magnitude checked — the three habits that keep constant-heavy problems correct.
Frequently asked questions
Do I need to memorize physical constants?
Memorize g ≈ 9.81 m/s² and the rough magnitude of the constants you use often. Precise values are best looked up in a reference; knowing the approximate size lets you catch a mistyped value.
How do I avoid power-of-ten errors with constants?
Use your calculator's scientific-notation key rather than typing out '× 10 ^', and when combining constants, handle the mantissas and exponents separately before recombining.
Why do constants have units?
The units make the equation dimensionally consistent. A constant like G carries units so that combining it with SI quantities yields the correct unit for the result. Carrying units through is a free error check.
How many significant figures should I keep?
No more than the least precise value in the calculation. Match your answer's precision to the least-precise input and round only at the end.