10 Important Equations That Help Explain the World
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In this article
Equations express relationships between quantities. The following selection introduces ideas used in mathematics and science; it is not an official ranking of the ten most influential equations.
Ten Equations
| Equation | Meaning and Important Condition |
|---|---|
| a² + b² = c² | Pythagoras’ theorem for a right-angled triangle; c is the hypotenuse. |
| F_net = ma | Net force equals mass times acceleration in the usual constant-mass Newtonian model. |
| F = Gm₁m₂/r² | Gravitational attraction between point masses, or suitable spherical bodies, separated by distance r. |
| K = ½mv² | Kinetic energy in the non-relativistic model. |
| W = Fd | Work for a constant force acting along the displacement. |
| P_avg = W/Δt | Average power: work done divided by elapsed time. |
| V = IR | Voltage, current and resistance; constant resistance describes ohmic behaviour. |
| v = fλ | Wave speed equals frequency multiplied by wavelength. |
| pV = nRT | Pressure, volume, amount and absolute temperature in the ideal-gas model. |
| E₀ = mc² | The relationship between rest energy and mass; c is the speed of light in vacuum. |
How to Read Them
Identify each symbol, use compatible units and check the assumptions before calculating. Similar-looking letters can mean different things: V can mean voltage in one equation and volume in another.
Tip: Learning when an equation applies is as important as memorising it.
