Physics Equations Calculator
Rearrange and solve the density, pressure, energy, work and power formulas, with the working.
See it happen: Forces & acceleration
Learn this properly
Lessons from GCSE Combined and Separate Science on this topic: worked steps, then exam-style questions with new numbers every time.
- Energy stores, transfers and kinetic energyEnergy stores, transfers and efficiencyFree
- PowerEnergy stores, transfers and efficiencyFree
- The equations: learn, choose and rearrangeRequired practicals, maths skills and the equationsPlus
See the whole courseThe full course, topic tests and mock papers come with Plus. See Plus
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.
About this tool
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.
Tips
- 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.