Physics Calculators

Physics calculators implement the fundamental laws of nature — Newton's laws of motion, conservation of energy and momentum, thermodynamics, electromagnetism, and relativity — to solve quantitative problems across all branches of classical and modern physics. From calculating the velocity of a projectile to the energy stored in a magnetic field, these tools make physical reasoning accessible and precise.

Physics is the most fundamental of the natural sciences, describing the behavior of matter and energy at all scales from subatomic particles to the structure of the universe. Its quantitative predictions are among the most precisely verified in science: the anomalous magnetic moment of the electron is predicted by quantum electrodynamics to better than 1 part in 10¹⁰ and confirmed experimentally to the same precision.

Classical mechanics — developed by Galileo, Newton, and their successors in the 17th and 18th centuries — describes the motion of macroscopic objects at speeds well below the speed of light. Newton's three laws of motion and the law of universal gravitation unified terrestrial and celestial mechanics, enabling prediction of planetary orbits, artillery trajectories, and ocean tides with a single mathematical framework.

Energy conservation is one of the deepest principles in physics. The total energy of an isolated system is constant, though it transforms between kinetic, potential, thermal, chemical, nuclear, and other forms. Understanding these transformations is essential for engineering efficient machines, analyzing collisions, and designing energy systems. Our physics calculators handle energy conversions, mechanical advantage calculations, and thermodynamic efficiency problems.

Kinematics describes the geometry of motion — position, velocity, acceleration, and time — without reference to the forces causing that motion. The four kinematic equations for constant acceleration provide a complete description of uniformly accelerated motion in one dimension.

Projectile motion — the two-dimensional motion of an object launched at an angle with only gravity acting on it — is the superposition of constant horizontal velocity and vertical free-fall. The range R = (v₀² × sin 2θ) / g, where v₀ is the launch speed, θ is the launch angle, and g = 9.81 m/s² is gravitational acceleration. Maximum range occurs at θ = 45° in the absence of air resistance.

Circular motion involves constant-speed motion along a circular path, requiring centripetal acceleration directed toward the center: a = v²/r, where v is the tangential speed and r is the radius. The centripetal force F = mv²/r must be provided by some agent — gravity for orbital motion, tension for a ball on a string, friction for a car navigating a curve.

Newton's second law, F = ma, relates the net force on an object to its mass and the resulting acceleration. Forces are vectors — they have both magnitude and direction — and must be added vectorially. When multiple forces act on an object, only the net (resultant) force determines the acceleration.

Work is the transfer of energy by a force: W = F × d × cos θ, where θ is the angle between the force and displacement vectors. Positive work transfers energy to the object; negative work removes energy. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv² − ½mv₀².

Conservation of energy: in an isolated system, total mechanical energy (KE + PE) is conserved when only conservative forces act. When an object falls a height h: the loss in gravitational PE equals the gain in KE: mgh = ½mv² (ignoring air resistance), giving v = √(2gh). This is valid regardless of the path taken — energy conservation is path-independent for conservative forces.

Linear momentum p = mv is the product of mass and velocity. Newton's second law in its most general form is: F_net = dp/dt (the net force equals the rate of change of momentum). The impulse-momentum theorem states that the impulse (force × time) equals the change in momentum: J = FΔt = Δp = mΔv.

Conservation of momentum applies when the net external force on a system is zero: the total momentum before a collision equals the total momentum after. In elastic collisions, both momentum and kinetic energy are conserved. In perfectly inelastic collisions, the objects stick together (maximum kinetic energy lost while momentum is conserved). In partially inelastic collisions, some energy is lost to deformation, heat, and sound.

Electric charge is the source of electric and magnetic fields. Coulomb's law describes the force between two point charges: F = k × q₁q₂/r², where k = 8.99 × 10⁹ N·m²/C² is Coulomb's constant. Like charges repel; unlike charges attract. The force falls off as the square of the distance.

Electric potential energy and voltage (electric potential) describe the energy landscape for charges. A charge q in an electric field experiences force F = qE, and potential energy U = qV. Electric current I = charge/time (amperes), voltage V = energy/charge (volts), and resistance R = V/I (ohms, Ohm's Law). Power P = IV = I²R = V²/R (watts).

Magnetic fields are produced by moving charges (current) and affect moving charges. The force on a charge q moving at velocity v in a magnetic field B is F = qv × B (the cross product gives force perpendicular to both velocity and field). Faraday's law of induction states that a changing magnetic flux through a loop induces an EMF (voltage) proportional to the rate of change.