Physics Formula Calculator
Pick a formula, choose which quantity to find, enter the rest in any unit — and get the rearranged formula, SI conversion and full substitution working.
To solve a physics numerical, write the formula, rearrange it for the unknown, convert every value to SI units, then substitute. From v = u + at the acceleration is a = (v − u) ÷ t. A car reaching 72 km/h, which is 20 m/s, from rest in 5 s has a = (20 − 0) ÷ 5 = 4 m/s².
Find a formula
Search by name, symbol or topic — e.g. “lens”, “KE”, “echo”.
First equation of motion
Step-by-step working
All formulas — quick reference
Tap any formula to open it in the calculator. Print it as a one-page revision sheet.
Solve numericals the exam way
Board examiners give marks for the formula, the substitution and the unit. This calculator writes all three for you so you can check your own working.
Pick a formula
Search or filter by topic — motion, force, energy, pressure, electricity, optics, waves or heat.
Choose the unknown
Tap any symbol under “Solve for”. The formula is rearranged for it automatically.
Enter values in any unit
km/h, grams, cm, minutes, kJ… Everything is converted to SI before substituting.
Read the working
See the rearranged formula, conversions, substitution and the final answer with its unit.
Always convert to SI first
Substitute only SI units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K).
- km/h → m/s: divide by 3.6 (72 km/h = 20 m/s)
- g → kg: divide by 1000 · cm → m: divide by 100
- 1 kWh = 1 unit = 3.6 × 10⁶ J
Rearranging a formula
Do the same operation on both sides until the unknown is alone. From v = u + at:
subtract u → v − u = at, divide by a → t = (v − u) ÷ a.
For squared quantities, take the square root at the end: v = √(u² + 2as).
Mirror and lens signs
Mirror: 1/f = 1/v + 1/u, m = −v/u. Lens: 1/f = 1/v − 1/u, m = v/u.
Negative m → real and inverted image. Positive m → virtual and erect. Lens power P = 1/f with f in metres (unit: dioptre, D).
Significant figures
Give the answer to about as many significant figures as the data — usually 3 or 4. Very large or small values are written in scientific notation, like 6.674 × 10⁻¹¹.
Physics Formula Calculator — your questions
How do I convert km/h into m/s?
Divide by 3.6, because 1 km/h = 1000 m ÷ 3600 s. So 72 km/h = 72 ÷ 3.6 = 20 m/s and 54 km/h = 15 m/s. To go the other way, multiply by 3.6. Always convert to SI units before substituting into a formula, or the answer will come out in the wrong unit.
What are the three equations of motion?
For uniform acceleration they are v = u + at, s = ut + ½at² and v² = u² + 2as, where u is the initial velocity, v the final velocity, a the acceleration, t the time and s the distance. A fourth useful form, s = (u + v)t ÷ 2, is handy when the acceleration is not known.
How do you rearrange a formula to find a different variable?
Do the same operation to both sides until the unknown stands alone. From v = u + at, subtract u to get v − u = at, then divide by a to get t = (v − u) ÷ a. If the unknown is squared, take the square root at the very end, as in v = √(u² + 2as).
How should I write a physics numerical in the exam?
Write the formula first, then substitute the values with their units, then box the final answer with its unit. Marking schemes usually award credit separately for the formula, the substitution and the correctly stated answer, so you can still score even if the arithmetic slips at the last step.
What is one unit of electricity in joules?
One commercial unit of electricity is one kilowatt-hour, which equals 3.6 × 10⁶ joules. A 1000 W appliance running for one hour therefore uses exactly one unit. This is why electricity bills are counted in kWh rather than joules — a joule is far too small a quantity for household use.
What are the sign conventions for the mirror and lens formulas?
The mirror formula is 1/f = 1/v + 1/u with magnification m = −v/u; the lens formula is 1/f = 1/v − 1/u with m = v/u. Under the New Cartesian convention the object sits on the left, so u is always negative. A negative m means a real, inverted image; a positive m means a virtual, erect one.
How many significant figures should a physics answer have?
Give roughly as many significant figures as the data you were given, which is usually three or four. Writing every digit the calculator shows is not more accurate and can cost marks. Very large or very small results are better written in scientific notation, such as 6.674 × 10⁻¹¹ for the gravitational constant.