Physics equations calculator
Pick a physics formula, such as density, pressure, kinetic energy, work or power, enter what you know and get the missing quantity, rearranged with the working. For GCSE and A-level physics.
See it happen: Forces & acceleration
Learn this properly
Lessons from the Combined and Separate Science courses on this topic: worked steps, then exam-style questions with new numbers every time.
Formulas
| Density | ρ = m / V |
|---|---|
| Pressure | p = F / A |
| Kinetic energy | Eₖ = ½mv2 |
| Gravitational potential energy | Eₚ = mgh |
| Work done | W = Fs |
| Power | P = E / t |
Worked example
A 0.5 kg ball is dropped from 3.2 m. Ignoring air resistance, how fast is it moving just before it lands?
- Potential energy lost: mgh = 0.5 × 9.81 × 3.2 = 15.7 J.
- All of it becomes kinetic energy, so ½mv2 = 15.7 J.
- v2 = 2 × 15.7 / 0.5 = 62.8, so v = √62.8 ≈ 7.9 m/s.
Answer: About 7.9 m/s.
Common mistakes
- Using grams or centimetres: change to kg and m first.
- Forgetting to square the speed in ½mv2.
- Using g = 10 N/kg when the question gives 9.81, or the other way round.
- Mixing up work done, an energy in J, with power, the energy per second in W.
How it works
This calculator covers six formulas that come up again and again in physics: density, pressure, kinetic energy, gravitational potential energy, work done and power. Fill in every quantity except the one you want and it rearranges the formula, substitutes your values and gives the answer in SI units. It is a good way to check a rearrangement you have done by hand.
- Pick a tab: Density, Pressure, Kinetic energy, Potential energy, Work done or Power.
- Fill in all the quantities except the one you want to find. Leave that box empty.
- Choose units where there is a choice, such as g or kg, cm3 or m3, and km/h or m/s.
- Read the rearranged formula, the substitution with your values and the answer with its SI unit.
Tips
- The formulas: ρ = m/V, p = F/A, Ek = ½mv2, Ep = mgh, W = Fd and P = E/t. Check you are on the right tab before entering numbers.
- Kinetic energy depends on v2, so doubling the speed makes the energy four times bigger. A 2 kg mass at 3 m/s has Ek = ½ × 2 × 32 = 9 J.
- g is set to 9.81 N/kg. If your course or exam uses 9.8 or 10 N/kg, change it so your answers match the mark scheme.
- To find v from kinetic energy, the rearrangement is v = √(2Ek / m). Squares and square roots are where most rearranging mistakes happen.
FAQ
- Why do the units matter?
- The formulas only work in SI units: kilograms, metres, seconds, newtons and joules. The unit choices convert common inputs for you, such as grams to kilograms or km/h to m/s, so the answer comes out in the right unit.
- Can I use it to rearrange formulas?
- Yes. Leave any one quantity empty and the calculator shows the formula rearranged for it before substituting. For example, Ep = mgh becomes h = Ep / mg when you want the height.
- What is the difference between work done and power?
- Work done is the energy transferred when a force moves something, W = Fd, measured in joules. Power is how quickly energy is transferred, P = E/t, measured in watts. One watt is one joule per second.