Physics Calculator

About Our Physics Calculators

Physics calculators on AI Calculator cover the equations students and engineers reach for most often: classical mechanics (kinematics, projectile motion, rotational motion), oscillations and waves (pendulum period, wave speed and frequency, Doppler shift), thermodynamics (ideal gas law, first-law energy balance), optics (Snell’s law, lens and mirror equations), electromagnetism (Coulomb’s law, Ohm’s law in physics form), and a small set of special relativity and quantum results (E = mc², de Broglie wavelength). Each tool shows the equation it is solving, the SI units of every input, and a worked example so the page also serves as a quick refresher when you have forgotten which constant goes where. The PDF report from each page includes the derivation step, so you can attach it to a problem set or a lab report.

Calculators in This Physics Suite

• Momentum Calculator Work & Power Calculator Wavelength Calculator Acceleration Calculator Speed Calculator Potential Energy Calculator Free Fall Calculator Density Calculator Friction Calculator Pressure Calculator Centripetal Force Calculator Hooke's Law Calculator Escape Velocity Calculator Impulse Calculator Gravitational Force Calculator Angular Velocity Calculator Terminal Velocity Calculator Force Calculator Projectile Motion Calculator — range, maximum height, time of flight, and trajectory for a projectile launched at angle θ with initial velocity v₀, neglecting air resistance.
• Kinetic Energy Calculator — translational kinetic energy KE = ½mv² with optional rotational term ½Iω² for a rigid body.
• Simple Pendulum Calculator — period T = 2π√(L/g) for the small-angle approximation, with a higher-order correction available for larger amplitudes.
• Photon Energy Calculator — photon energy from wavelength or frequency via E = hf = hc/λ, in joules, electronvolts and kJ/mol.
• Snell's Law Calculator — angle of refraction from n₁sinθ₁ = n₂sinθ₂, with total internal reflection and critical-angle detection.
• Doppler Effect Calculator — observed sound frequency from source and observer motion, f′ = f(v+vₒ)/(v−vₛ), with the pitch shift.

Key Formulas at a Glance

For a projectile fired at angle θ with initial speed v₀ on a flat surface (g = 9.81 m/s²): range R = v₀² sin(2θ) / g, maximum height H = v₀² sin²(θ) / (2g), and time of flight T = 2v₀ sin(θ) / g. The maximum-range angle for level ground is 45°; for a launch above the landing point the optimal angle is less than 45° and the calculator lets you specify the launch height to handle that case.

For a simple pendulum of length L (m), the small-angle period is T = 2π √(L/g). This expression is good to within 1% for amplitudes up to about 15°. For larger amplitudes a better expression is T = 2π √(L/g) × (1 + θ₀²/16 + 11θ₀⁴/3072 + …), the leading terms of an elliptic-integral expansion.

Kinetic energy of a translating point mass is KE = ½mv². For a rigid body that is also rotating, the total kinetic energy is KE_total = ½mv_cm² + ½Iω², where I is the moment of inertia about the centre of mass and ω is the angular velocity. For a solid sphere I = (2/5)mr²; for a thin hoop I = mr²; for a uniform rod about its centre I = (1/12)mL².

Where These Calculators Help

For high-school and early-undergraduate physics, the projectile and pendulum calculators are useful for checking homework against an authoritative reference and for visualising how the answer changes with each input — try varying the launch angle from 30° to 60° on the projectile calculator and watch how the range curve peaks at 45°. For lab work, the pendulum calculator is a quick way to check whether your measured period matches the small-angle prediction, which is a common first lab in mechanics. For early-career engineers, the kinetic energy calculator is handy for sizing flywheels and rotating machinery (KE storage = ½Iω²; flywheel inertia from rim mass).

Frequently Asked Questions

Why is g taken as 9.81 m/s² and not 10?
Standard gravity at the Earth’s surface is g = 9.80665 m/s², usually rounded to 9.81 in engineering work. Using g = 10 introduces about 2% error, which is fine for back-of-envelope estimates but not for laboratory calculations. The calculators on this site let you set g manually if you are computing for a different latitude or a different planet.

Does the projectile calculator account for air resistance?
No — it solves the standard parabolic trajectory in vacuum. For real-world projectiles with significant drag (sports balls, ballistics), the trajectory deviates from the parabola and a numerical solver with drag coefficient is needed. The calculator will note when air drag becomes significant for the parameters you have entered.

What’s the difference between a simple and a physical pendulum?
A simple pendulum models the bob as a point mass at the end of a massless string. A physical pendulum has its mass distributed along its length and uses period T = 2π √(I / (mgd)), where d is the distance from the pivot to the centre of mass and I is the moment of inertia about the pivot.

Can these calculators be used for SI and CGS units?
The default is SI; the input fields support unit conversion to imperial (feet, ft/s, lbf) where appropriate. CGS (cm-gram-second) is not directly supported in the UI, but you can manually convert before entering.

Related calculator categories: Electrical engineering · Mechanical engineering · Chemical & process · Civil & structural · Engineering formulas reference