Physics Calculator Online

Push a book across a table and stop pushing — it slows down. That deceleration is a force in disguise, and the relationship between force, mass, and acceleration is one of the most useful patterns in all of physics. Isaac Newton formalized it: the net force on an object equals its mass multiplied by its acceleration. Every other equation in this tool is an extension of that core insight applied to specific situations.

Kinetic energy measures how much work an object can do by virtue of its motion. A car at highway speed carries enough kinetic energy to lift itself over a two-story building — that is why speed matters so much in crash physics. The equation squares velocity, which means doubling speed quadruples energy, not doubles it. This non-linear relationship is why speed limits are not arbitrary.

Power is the rate at which work is done — not how much total energy is used, but how fast it is delivered. A 100-watt bulb running for 10 hours uses the same total energy as a 1,000-watt microwave running for one hour. The distinction matters whenever timing is part of the problem: engines, motors, and human muscles are all rated by power because their useful output depends on how quickly they can deliver energy, not just how much they store.

Use this tool when you have two of the three variables in a standard mechanics relationship and need the third. It is appropriate for homework checks, back-of-envelope engineering estimates, unit verification, and quick sanity checks on published figures. Athletes, cyclists, and coaches use kinetic energy and power calculations to benchmark physical output against lab-measured standards.

Do not use this tool when your problem involves variable acceleration — for example, a rocket burning fuel changes mass over time, so F = ma produces only an instantaneous value, not an average over the burn. Similarly, drag force is velocity-dependent, so a falling object does not have constant acceleration; this tool's kinematic equation will overestimate final velocity in air.

For relativistic speeds (above roughly 10% of the speed of light, or 30,000 km/s), Newtonian mechanics breaks down. KE = 0.5mv2 underestimates true kinetic energy at those velocities. This tool is strictly classical mechanics for everyday speeds and masses.

The most common mistake is mixing units. Entering mass in grams instead of kilograms produces a force in millinewtons rather than newtons — the calculation runs fine but the answer is off by a factor of 1,000. Always confirm your units before reading the result.

A second frequent error is treating weight and mass as interchangeable. Weight is a force (in Newtons), not a mass. A 70 kg person has a weight of 686.7 N on Earth. If you enter 70 into the force field when the problem specifies mass, every derived quantity will be wrong. The distinction matters the moment you leave Earth's surface or need precision.

For the velocity equation, users often forget that initial velocity must be included — setting it to zero is valid only if the object genuinely starts from rest. Omitting it or leaving the field blank when the object already has speed produces an underestimate of final velocity. The equation v = u + at requires all three: initial speed, acceleration, and time.

Newton's second law: F = ma. Rearranged for mass: m = F/a. Rearranged for acceleration: a = F/m. These three are algebraically identical — choose which variable you are solving for based on which two you know.

Kinematic final velocity: v = u + at. Here u is initial velocity (m/s), a is acceleration (m/s2), and t is time (s). This assumes constant acceleration — the equation breaks down if acceleration changes during the interval. For non-uniform acceleration you need calculus (the integral of acceleration over time).

Kinetic energy: KE = 0.5 x m x v2. Potential energy: PE = mgh, where g is 9.81 m/s2 at Earth's surface. By conservation of energy, KE + PE stays constant for an object in free fall with no air resistance — so you can set 0.5mv2 = mgh to find the velocity at any height, which cancels mass entirely. Power: P = W/t, where W is work in Joules and t is time in seconds. One watt equals one joule per second.

Every equation here assumes the system is inertial — no rotating reference frame, no gravity gradient. The potential energy formula PE = mgh is a linearization valid only when height change is small compared to Earth's radius (about 6,371 km). At large altitudes, PE = -GMm/r is the correct expression, and the simple formula overestimates energy by measurable amounts above roughly 100 km. Similarly, kinetic energy in the formula assumes rigid body point-mass behavior — rotational kinetic energy (0.5 x I x omega2) is entirely separate and must be added when objects spin.