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Physics & Engineering

Twenty-six physics calculators across seven topical clusters: mechanics, rotational and periodic motion, waves and optics, circuits, fluids, thermal, and modern physics. Formulas shown, units checked, all cross-linked.

Physics calculations on this site are formula-grounded, unit-checked, and cross-linked. Each tool starts from a textbook equation (Newton's second law, Ohm's law, the thin lens equation, Bernoulli's, the first law of thermodynamics) and shows the substitution step by step so you can verify by hand. Constants come from NIST CODATA: g, c, G, k_B, ε₀, h, the works, held to at least six significant figures where accuracy matters. Twenty-six calculators cover seven topical clusters: kinematics and mechanics, rotational and periodic motion, waves and optics, electricity and circuits, fluid mechanics, thermal and heat transfer, and modern physics. None of them require sign-in, none upload your numbers, and every page lists the assumptions that govern when its answer stops being trustworthy. The shortlist below is the fastest path to the right tool.

Which Calculator Do I Need?

Scan for the question that matches yours. Each cluster gets a short narrative below; this list is the table of contents.

How the Clusters Fit Together

Kinematics & mechanics

Newtonian mechanics is five tools deep. For pure kinematics where you know acceleration is constant, the SUVAT solver picks the right one of the five constant-acceleration relations for 1D problems. The projectile motion calculator extends that to 2D, splitting motion into independent horizontal and vertical components. Force-side work begins at force, work, and power, which pairs F = ma with W = F·d·cos(θ), and the friction and inclined plane calculator handles slope-with-friction problems. Energy bookkeeping (kinetic and gravitational potential) lives in the energy calculator. The boundary between these last two is your call: energy methods skip integration when you only care about endpoints, force methods are required when you need acceleration or trajectory.

Rotational, periodic, and orbital

Anywhere a system repeats, the math is the same: an angular frequency ω, a period T = 2π/ω, a frequency f = 1/T. The circular motion calculator handles uniform rotation around a fixed center, with inward force F_c = mv²/r and acceleration a_c = ω²r. Replace centripetal force with a restoring force proportional to displacement and you get simple harmonic motion: springs (ω = √(k/m)), small-angle pendulums (ω = √(g/L)), LC circuits, and any oscillator near a potential minimum. Apply Kepler's laws to the special case of inverse-square gravity and you get the orbital period and gravity field calculator, with T² ∝ a³ falling out of energy conservation in a 1/r potential. Same conceptual machinery, different physical sources.

Waves & optics

Wave physics splits along medium and detection. The waves calculator is the general engine: v = fλ, ω = 2πf, k = 2π/λ, with phase ϕ = kx − ωt + ϕ₀. Sound is a longitudinal wave in air, and human hearing spans roughly 20 Hz to 20 kHz with intensity logged on the decibel scale (SPL = 20 log₁₀(p/p_ref), where p_ref = 20 μPa). The sound intensity and decibel calculator walks through dB conversions, distance attenuation (a 6 dB drop per doubling of distance for a point source in free field), and OSHA exposure limits. Optics is the geometric-ray limit of light. The thin lens equation calculator covers single-element setups (1/f = 1/d_o + 1/d_i, sign conventions, magnification), and the lens and mirror combination calculator chains those equations across telescopes, microscopes, and telephoto pairs.

Electricity & circuits

Start with the static problem of point charges. The Coulomb's law calculator handles forces and fields (F = kq₁q₂/r², k ≈ 8.988 × 10⁹ N·m²/C²) with proper vector superposition for multi-charge arrangements. Once charges move, you're in circuit territory. Ohm's law gives V = IR for resistive networks, plus series and parallel combinations. For transients, the RC circuit time constant calculator models charging and discharging through τ = RC (about 63% of the way after one τ, more than 99% after five). Inductive transients and resonance live in the RL/RLC circuit calculator, with ω₀ = 1/√(LC) and Q = (1/R)·√(L/C). Real systems waste energy as heat, and the power and efficiency calculator handles η = P_out/P_in for motors, supplies, and DC-DC converters.

Fluid mechanics

Three tools cover the static-and-moving regimes. For static fluids, the fluid pressure and hydrostatic force calculator gives pressure at depth (P = ρgh + P_atm) and total force on submerged surfaces, with the centroid and center-of-pressure formulas you need for dam, gate, and tank-wall analysis. For ideal moving flow, the Bernoulli equation calculator applies P + ½ρv² + ρgh = constant along a streamline (assumes incompressible, inviscid, steady flow with no shaft work). The validity of those assumptions hinges on the Reynolds number and flow regime calculator, where Re = ρvD/μ tells you whether viscous effects matter. Below Re ≈ 2300 in a pipe, flow is laminar and Bernoulli plus Hagen-Poiseuille applies. Above Re ≈ 4000, turbulence takes over and you switch to friction-factor correlations (Moody chart, Colebrook equation).

Thermal & heat transfer

Materials respond to temperature in two ways: they expand and they conduct heat. The thermal expansion calculator gives ΔL = L₀ α ΔT for linear expansion (α ≈ 12 × 10⁻⁶ /K for steel, 23 × 10⁻⁶ /K for aluminum, about 8 × 10⁻⁶ /K for concrete) and the area or volume analogues using 2α and 3α. Don't skip expansion joints in a 30 m steel rail: a 50 K swing gives 18 mm of growth. The heat transfer (conduction) calculator handles steady-state Fourier conduction (q = kA·ΔT/L) and multi-layer walls using thermal resistance networks (R = L/(kA), resistances in series add). For practical exchangers, the LMTD helper computes the log-mean temperature difference for counterflow and parallel-flow configurations and inverts it to give the required area for a target duty: Q = U·A·LMTD.

Modern physics & astrophysics

Three tools where Newtonian intuition either fails or needs serious supplementation. The relativistic effects calculator computes time dilation, length contraction, and the Lorentz factor γ = 1/√(1 − v²/c²) for any v < c. Below 0.1c the corrections are noise. Above 0.1c they're unavoidable, and at GPS-orbit speeds (~3.87 km/s) the combined special- and general-relativistic offsets accumulate to +38.6 μs/day if you don't compensate. The escape velocity calculator handles v_esc = √(2GM/R) for Earth (11.2 km/s), Moon (2.4 km/s), Mars (5.0 km/s), or any custom body, using NASA-published values for M and R. The thermodynamics calculator covers classical thermo: Carnot efficiency (η = 1 − T_c/T_h), engine cycles on P-V diagrams (Otto, Diesel, Rankine), and the first and second laws applied to closed systems. For chemistry-flavored thermo, see the related Gibbs free energy calculator.

Physics Glossary: Constants and Conventions

Constants and conventions used across the calculators. Every numerical value below comes from NIST CODATA or the post-2019 SI redefinitions where applicable.

SI base units.
Meter, kilogram, second, ampere, kelvin, mole, candela. Every other physical unit is built from these.
Standard gravity g.
9.80665 m/s² (ISO defined). Use 9.81 for homework, 9.80665 for instrument calibration.
Speed of light c.
299,792,458 m/s exactly (defines the meter since 1983).
Gravitational constant G.
6.67430 × 10⁻¹¹ N·m²/kg² (CODATA 2018).
Coulomb constant k.
1/(4πε₀) ≈ 8.98755 × 10⁹ N·m²/C².
Vacuum permittivity ε₀.
8.85419 × 10⁻¹² F/m.
Boltzmann constant k_B.
1.380649 × 10⁻²³ J/K (exact since the 2019 SI redefinition).
Avogadro's number N_A.
6.02214076 × 10²³ /mol (exact since 2019).
Planck's constant h.
6.62607015 × 10⁻³⁴ J·s (exact since 2019).
Standard atmosphere.
101,325 Pa = 1 atm = 760 mmHg.
Absolute temperature.
Measured in kelvin from absolute zero. 0 K = -273.15 °C.
Sign conventions in optics.
Positive image distance means a real image on the opposite side of a lens from the object; negative means virtual on the same side. Mirrors flip the rule. Each calculator that uses sign conventions states which one applies.
Vectors vs. scalars.
Force, velocity, current density, and electric field have direction. Mass, energy, temperature, and work don't. Mixing the two is the most common source of sign errors in homework.

How We Build These Tools

Calculation formulas across these tools are verified by our mathematics, engineering, and scientific team (Wahidullah Habib, Ishfaq Ur Rahman, Abbas Kalim Khan, Bilal Khan) and sourced from peer-reviewed and standards-body references: NIST CODATA for fundamental constants, NASA JPL for planetary masses and radii, OpenStax University Physics for canonical undergraduate derivations, HyperPhysics for cross-checks, and ASME / ASHRAE handbooks for engineering correlations. Every calculator implements the textbook formula directly in JavaScript and shows its work. Nothing is precomputed or memoized in a way that hides the math. We re-verify against the source when we update a tool, and the "Last Updated" badge on each page reflects the most recent pass. Pages that have been through individual verifier review carry a byline directly under the H1 with the reviewer's name, role, and review date, so you can tell at a glance which calculator formulas were checked by which team member. If you find an error, email contact@everydaybudd.com with the inputs and what you expected. Reader reports have caught several real bugs (a sign flip in the lens-mirror combination, microfarad-vs-farad unit confusion in the RC time constant tool), and we keep doing that.

Physics & Engineering Guide

Editorial review: April 23, 2026

What you can do in Physics & Engineering

  • •Calculate force, work, and power with incline plane analysis and friction coefficients
  • •Analyze projectile motion with trajectory visualization, range, max height, and flight time
  • •Solve circuit problems using Ohm's law, Kirchhoff's rules, and series/parallel combinations
  • •Compute thermodynamic properties: heat transfer, thermal expansion, and ideal gas behavior
  • •Model wave phenomena: frequency, wavelength, interference, and Doppler effects
  • •Analyze optical systems with lens equations, magnification, and ray diagrams

Accuracy, assumptions, and sources

  • •All calculators use SI units by default (meters, kilograms, seconds, kelvin). Unit converters are provided.
  • •Physical constants use NIST CODATA values (g = 9.80665 m/s², c = 299,792,458 m/s, G = 6.674e-11 N·m²/kg², etc.).
  • •Ideal conditions are assumed unless stated: no air resistance, frictionless surfaces, ideal gases, paraxial optics, inviscid fluids.
  • •Significant figures are preserved in calculations. Results show appropriate precision for inputs.
  • •Wave and optics calculators assume linear, small-angle approximations where applicable.
  • •Thermal calculations assume constant specific heat unless temperature-dependent tables are provided.

Pick the right calculator fast

Common mistakes to avoid

  • •Mixing SI and imperial units in the same calculation. Convert all values to consistent units first.
  • •Forgetting to use radians for angular calculations. Most physics formulas require radians, not degrees.
  • •Ignoring sign conventions for vectors (forces, velocities). Pay attention to positive/negative directions.
  • •Applying SUVAT when acceleration isn't constant. Use calculus or numerical methods instead.
  • •Using thin-lens approximations for thick lenses or systems with significant aberrations.
  • •Confusing voltage drops in series with current splits in parallel circuits.
  • •Neglecting friction in real-world mechanical problems.
  • •Assuming ideal gas behavior at high pressures or low temperatures where it breaks down.

Editorial policy

  • ✓Calculators provide educational estimates, not licensed engineering analysis or professional design.
  • ✓Formulas match standard physics references (Halliday, Serway, Young & Freedman, Hecht for optics, Incropera for heat transfer).
  • ✓Most tools work without sign-in. See the Privacy Policy for analytics, advertising, and cookie disclosures.
  • ✓Physical constants are referenced from NIST CODATA. We update when official values change.
  • ✓Found an error? Email contact@everydaybudd.com and we'll fix it promptly.
  • ✓Tools are updated when physics education standards or calculation methods improve.

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Frequently Asked Questions

What's the difference between mass and weight?

Mass is the amount of matter in an object (kilograms, scalar); weight is the gravitational force on that mass (newtons, vector). On Earth, weight W = mg with g ≈ 9.81 m/s². Take a 70 kg person to the Moon and the mass stays 70 kg, but weight drops from about 686 N to 113 N because lunar g is 1.62 m/s². Mass shows up in Newton's second law (F = ma) and momentum (p = mv). Weight shows up in any free-body diagram as the downward arrow on a body in a gravitational field. People conflate the two because bathroom scales show mass while actually measuring weight, which only works if g is fixed. See Force, Work, and Power Calculator and Friction and Inclined Plane Calculator.

Why is g = 9.81 m/s² on Earth?

Surface gravity falls out of g = GM/R² with Earth's mass M = 5.972 × 10²⁴ kg, equatorial radius R = 6.371 × 10⁶ m, and the gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg². ISO defines standard gravity as exactly 9.80665 m/s², but real values vary from about 9.78 at the equator (you sit farther from Earth's center and centrifugal effects from rotation reduce apparent g) to 9.83 at the poles. Altitude knocks it down by roughly 3 × 10⁻⁶ m/s² per meter you climb. For homework, 9.81 is fine. Use 9.80665 if you're calibrating instruments or working to four-digit precision. See Orbital Period and Gravity Field Calculator and Escape Velocity Calculator.

What are the SI base units in physics?

Seven base units: meter (m, length), kilogram (kg, mass), second (s, time), ampere (A, electric current), kelvin (K, thermodynamic temperature), mole (mol, amount of substance), candela (cd, luminous intensity). Every derived unit is built from these. Newton is kg·m/s², joule is kg·m²/s², watt is kg·m²/s³, volt is kg·m²/(A·s³). Since the 2019 SI redefinition, all seven are tied to fixed numerical values of fundamental constants (Planck's constant defines kg, the speed of light defines m, the elementary charge defines A) instead of physical artifacts. The old kilogram prototype in Sèvres is now a museum piece. For unit consistency in any calculator, work in SI base or coherent derived units. See the full physics calculators directory.

What does 'centripetal' actually mean?

Centripetal means "directed toward the center" (Latin centrum + petere, "to seek"). A centripetal force is whatever physical agent pulls an object on a curved path inward, toward the instantaneous center of curvature. It's not a separate type of force, it's a role. For a car cornering, friction plays the role. For a satellite, gravity plays the role. The magnitude is F_c = mv²/r = mω²r. Don't confuse centripetal with centrifugal: centrifugal is the apparent outward push you feel in a rotating frame, and it doesn't exist in an inertial frame. The Earth-frame physics has only the inward (centripetal) force; the outward sensation is your inertia trying to go straight while the seat pushes you sideways. See Circular Motion Calculator and Orbital Period Calculator.

How are voltage, current, and resistance related?

Ohm's law: V = IR, where V is voltage in volts, I is current in amperes, R is resistance in ohms. Voltage is the electrical potential difference per unit charge, current is the rate of charge flow, resistance is the opposition. Power follows from any two: P = VI = I²R = V²/R. Real components are ohmic (linear) only over a limited range. LEDs and incandescent bulbs are nonlinear, so V = IR fails for them and you need an I-V curve. In AC circuits, replace R with impedance Z, which is complex and frequency-dependent: V = IZ, with capacitors and inductors contributing reactance instead of resistance. See Ohm's Law Calculator, RC Circuit Calculator, RL/RLC Circuit Calculator, and Power and Efficiency Calculator.

What's the difference between heat and temperature?

Heat is energy in transit (joules) between systems at different temperatures; temperature is a measure of average kinetic energy of particles in a system (kelvin or Celsius). A bathtub of lukewarm water has more total heat content than a cup of boiling water, even though the cup is hotter. The relationship for sensible heating is Q = mcΔT, where c is specific heat capacity (about 4186 J/kg·K for liquid water). Phase changes absorb or release heat without a temperature change: melting one kilogram of ice at 0°C absorbs 334 kJ. The first law of thermodynamics tracks heat, work, and internal energy as ΔU = Q − W in physics convention. See Thermodynamics Calculator, Heat Transfer (Conduction) Calculator, Thermal Expansion Calculator, and the LMTD Helper.

What is the Lorentz factor and when does it matter?

The Lorentz factor γ = 1/√(1 − v²/c²) sets the size of relativistic effects. At v = 0.1c, γ ≈ 1.005 (a 0.5% correction). At v = 0.5c, γ ≈ 1.155. At v = 0.99c, γ ≈ 7.09. Below v/c ≈ 0.01 (about 3,000 km/s) the correction is under one part in 20,000 and Newtonian mechanics is fine. Above v/c ≈ 0.1 you can't ignore γ. Real cases where it shows up: GPS satellites (orbital v ≈ 3.87 km/s, where the gravitational redshift effect actually dominates and offsets clocks by +38.6 μs/day if uncorrected), atmospheric muons created at γ ≈ 10 reaching sea level instead of decaying at 660 m, particle accelerators where γ exceeds 7,000 at LHC energies. Length contracts by 1/γ; proper time dilates by γ. See Relativistic Effects Calculator.

Why is escape velocity independent of mass?

The escape velocity formula v_esc = √(2GM/R) contains the mass M of the gravitating body (Earth, Moon, etc.) but not the mass m of the escaping object. That's because both kinetic energy (½mv²) and gravitational potential energy (−GMm/r) scale linearly with m, so it cancels in the energy-conservation equation that gives v_esc. A baseball needs the same 11.2 km/s as a bowling ball to leave Earth permanently from the surface (ignoring atmospheric drag). What's not independent of mass is fuel: a heavier rocket needs more thrust to reach v_esc, governed by the Tsiolkovsky equation Δv = v_e ln(m_0/m_f). That's why staging is essential for chemical rockets, where exhaust velocities cap around 4.4 km/s for the best LOX/LH₂ engines. See Escape Velocity Calculator and Orbital Period Calculator.

What's the difference between Bernoulli's principle and Pascal's principle?

Pascal's principle says pressure applied to an enclosed incompressible fluid transmits equally in all directions, which is the basis of hydraulic jacks, brake systems, and any closed hydraulic circuit. Bernoulli's principle says along a streamline in steady, inviscid, incompressible flow, P + ½ρv² + ρgh stays constant; it's the basis of Pitot tubes, Venturi meters, and the lift on aircraft wings. They describe different regimes. Pascal applies to a static fluid where you push and the whole volume responds together. Bernoulli applies to a moving fluid where speeding up loses pressure and slowing down gains it. Both come from conservation laws (Pascal from force balance, Bernoulli from energy conservation along a streamline). See Bernoulli Equation Calculator and Fluid Pressure and Hydrostatic Force Calculator.

How do you tell if fluid flow is laminar or turbulent?

Compute the Reynolds number Re = ρvD/μ (equivalently vD/ν), where ρ is density, v is characteristic velocity, D is characteristic length (pipe diameter, plate length, sphere diameter), μ is dynamic viscosity, and ν is kinematic viscosity. For circular pipes, Re < 2300 is laminar (smooth, parallel streamlines). Between 2300 and 4000 you're in the transitional regime where flow oscillates between states. Re > 4000 is fully turbulent (chaotic eddies, much higher pressure drop, much higher mixing). Thresholds shift for other geometries: flat-plate boundary layers transition around Re ≈ 5 × 10⁵, open channels around Re ≈ 500. Water at 20°C through a 50 mm pipe at 0.5 m/s gives Re ≈ 25,000 (turbulent). Drag coefficients, heat-transfer rates, and pressure drops all change qualitatively at the transition. See Reynolds Number Calculator and Bernoulli Calculator.