Physics Tools

Physics Calculators for Students and Engineers

Physics problems span an enormous range — from classical Newtonian mechanics to relativistic time dilation and electromagnetic field calculations. This collection covers the most searched physics calculator topics: work and energy, torque, friction, fluid dynamics, optics, thermodynamics, and electromagnetism. All tools support both SI and imperial units and run entirely in your browser.

Mechanics: Work, Force, and Rotation

Work-energy calculations are central to mechanics at every level. The work-energy theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv₂² − ½mv₁². For a force applied at angle θ over distance d, W = F × d × cos θ. A 50 N force applied at 30° over 10 m does W = 50 × 10 × cos(30°) = 433 J. The Work-Energy Theorem Calculator solves for any variable and shows the energy conservation breakdown.

Torque problems involve force applied at a lever arm: τ = r × F × sin θ, where r is the distance from the pivot and θ is the angle between the force vector and lever arm. A 100 N force applied perpendicular to a 0.5 m wrench handle produces 50 N·m of torque. The Torque Calculator outputs in both N·m and ft·lb. For rotational systems, the Rotational Motion Calculator handles angular velocity (ω), angular acceleration (α), moment of inertia (I), and torque with shape presets for common objects (disk, ring, rod, sphere).

Friction and Springs

Friction force depends on the coefficient of friction and normal force: f = μN. For a 10 kg block on a surface with μ_k = 0.3, the kinetic friction force is f = 0.3 × (10 × 9.8) = 29.4 N. Static friction uses μ_s (higher than kinetic) and represents the maximum force before the object begins sliding. The Friction Calculator includes a material lookup table for common surface pairs. Hooke's law for springs (F = kx) connects spring constant k, displacement x, and force. The Spring Constant Calculator solves for k, F, x, or elastic potential energy (PE = ½kx²) and connects to the simple harmonic motion period T = 2π√(m/k).

Fluid Dynamics and Thermodynamics

Pascal's law states that pressure applied to an enclosed fluid is transmitted equally throughout: P = ρgh for pressure at depth h in a fluid of density ρ. At 10 m depth in water (ρ = 1000 kg/m³), gauge pressure = 1000 × 9.8 × 10 = 98,000 Pa ≈ 0.97 atm. The Fluid Pressure Calculator solves for gauge and absolute pressure with density and depth inputs.

Bernoulli's principle relates pressure, velocity, and height for ideal fluid flow: P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂. This explains why airplane wings generate lift (faster airflow over the top surface lowers pressure) and why water speeds up through a narrow pipe. The Bernoulli Equation Calculator solves for any of the six variables given the other five.

Specific heat calculations use Q = mcΔT, where m is mass, c is specific heat capacity, and ΔT is temperature change. Water's specific heat (4,186 J/kg·K) means heating 1 kg of water from 20°C to 100°C requires 4,186 × 1 × 80 = 334,880 J. The Specific Heat Calculator includes a material database and supports calorimetry problems with mixed materials. For heat engine efficiency, the Carnot Efficiency Calculator gives the theoretical maximum efficiency η = 1 − T_cold/T_hot.

Optics and Waves

Snell's law governs refraction at the boundary between two media: n₁ sin θ₁ = n₂ sin θ₂. Light entering water (n = 1.33) from air (n = 1.00) at 45° refracts to sin θ₂ = sin(45°)/1.33 = 0.532, giving θ₂ = 32.1°. When n₁ > n₂ and the angle exceeds the critical angle θ_c = arcsin(n₂/n₁), total internal reflection occurs — the principle behind fiber optic cables. The Snell's Law Calculator solves for any angle or refractive index and checks for total internal reflection. The Electromagnetic Spectrum Reference provides an interactive visualization of the full EM spectrum from radio waves to gamma rays with wavelength, frequency, energy, and typical sources for each region.

Electromagnetism

Magnetic fields from current-carrying conductors vary by geometry. For a long straight wire: B = μ₀I/(2πr). For a solenoid with n turns per meter: B = μ₀nI. For a circular loop of radius r: B = μ₀I/(2r) at the center. The Magnetic Field Calculator handles all three geometries with SI and customary unit support. For circuit analysis, the Circuit Calculator computes equivalent resistance, total capacitance, and equivalent inductance for series and parallel combinations, along with voltage divider ratios. The Electric Circuit Visualizer provides an interactive canvas-based circuit builder showing current and voltage at each element.

Special Topics

Terminal velocity occurs when drag force equals gravitational force: v_t = √(2mg/ρAC_d), where ρ is air density, A is cross-sectional area, and C_d is drag coefficient. A skydiver (m = 80 kg, A = 0.5 m², C_d = 1.0) has terminal velocity v_t = √(2×80×9.8/(1.225×0.5×1.0)) ≈ 50 m/s (180 km/h). The Terminal Velocity Calculator handles any combination of these inputs. For special relativity, the Time Dilation Calculator shows how time slows and length contracts at relativistic speeds: t' = t/√(1−v²/c²). At 80% the speed of light, γ = 1/√(1−0.64) = 1.67, so 1 year on the rocket is 1.67 years on Earth. The Physics Formulas Cheatsheet provides a printable, searchable reference covering all major topics.