Physics Calculator

One tool, many equations — and why it shows its work

Most physics problems at school level come down to plugging known values into a standard equation and rearranging to find the unknown. The arithmetic is rarely the hard part; the rearranging and the careful substitution are where mistakes creep in. This calculator handles both. You pick a category and a formula, tell it which variable you want to solve for, and enter the rest. It rearranges the equation algebraically, substitutes your numbers, and shows the worked formula alongside the answer — so it's a check on your own working, not a black box. Everything runs in your browser; nothing is sent anywhere.

What it covers

The formulas are grouped into six categories spanning the core of introductory mechanics, waves, and electricity:

• Kinematics — the three equations of motion: v = u + at, s = ut + ½at², and v² = u² + 2as.
• Forces — Newton's second law F = ma, weight W = mg, and friction F = μN.
• Energy — kinetic energy KE = ½mv², gravitational potential energy PE = mgh, and work W = Fd.
• Circular motion — centripetal acceleration a = v²/r and centripetal force F = mv²/r.
• Waves — the wave equation v = fλ and the frequency–period relationship f = 1/T.
• Electricity — Ohm's law V = IR and electrical power P = IV and P = I²R.

Each formula carries its own units, shown next to the inputs (m/s, N, J, Hz, V, A, Ω and so on), so you are reminded what SI quantity each box expects.

Solving for any variable, not just the obvious one

The real convenience is that you can solve for any term in an equation, not only the one it's usually written for. Take v² = u² + 2as. Choose "Final velocity" and it computes v = √(u² + 2as). Choose "Acceleration" instead and the same equation is rearranged on the fly to a = (v² − u²) / (2s). The "Solve for" dropdown lists every variable in the formula, and the input boxes update to ask for exactly the others. This means one formula entry replaces the several rearranged versions you'd otherwise keep in your head.

A worked example

A car accelerates from rest at 3 m/s² for 5 s. How far does it travel? Pick Kinematics, the formula s = ut + ½at², and solve for Displacement (s). Enter u = 0, a = 3, t = 5. The calculator substitutes into s = ut + ½at² = 0×5 + 0.5×3×5² and returns 37.5 m. Because it prints the substituted formula, you can confirm at a glance that it used your exact numbers — a habit worth keeping, because it catches the classic error of mistyping an input far more reliably than just trusting a final figure.

Constants and rounding you should know about

• Gravity is taken as 9.81 m/s². The weight formula W = mg and potential energy PE = mgh both use g = 9.81. If your textbook rounds to 9.8 or 10, expect a small difference in the last digits — that's the constant, not an error.
• Results are rounded to six decimal places. Answers are tidied to six places, which is plenty for schoolwork. For an exam, round the displayed value to the significant figures your question asks for.
• Impossible inputs are caught. If a calculation would divide by zero or produce a non-finite result — for instance solving for acceleration with zero displacement — the tool reports that it cannot solve rather than showing nonsense.

Common mistakes this helps you avoid

• Mismatched units. The formulas assume SI units throughout. If a distance is given in kilometres or a time in minutes, convert to metres and seconds first; the tool trusts the numbers you type and won't convert for you.
• Sign errors with deceleration. An object slowing down has a negative acceleration relative to its motion. Enter a = −3, not 3, or the kinematics result will point the wrong way.
• Confusing initial and final velocity. In the equations of motion, u is the starting speed and v the ending speed. Swapping them is the single most common slip — the labels next to each box spell out which is which.
• Forgetting the squared term. When solving by hand to check, remember that ½at² squares the time and ½mv² squares the velocity. The tool does this correctly; mental-arithmetic checks often don't.

Who it's for

This is built for students working through homework and revising for exams, where the goal is not just an answer but understanding the rearrangement that produced it. Teachers can use it to generate worked solutions, and anyone needing a quick, reliable evaluation of a standard physics relationship — converting frequency to period, finding a resistor's value from voltage and current, sizing a centripetal force — will find it faster than reaching for a scientific calculator and rearranging by hand.