Physics tools
Mechanics, energy, and rotational motion calculators
- custom
AI concept explainer (roadmap)
Planned: tutoring-style explanations.
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AI derivation generator (roadmap)
Planned: derivation sketches from law names.
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AI formula finder (roadmap)
Planned: match scenarios to standard equations.
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AI numerical solver (roadmap)
Planned: numeric checks with units.
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AI physics problem solver (roadmap)
Planned: guided solutions from text problems.
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AI quiz generator (roadmap)
Planned: generated MCQs by topic.
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AI weak-topic analyzer (roadmap)
Planned: patterns from attempt history.
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Angular acceleration
α = Δω / Δt.
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Angular velocity
ω = Δθ/Δt or ω = v/r (no slip).
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Archimedes’ principle
Same as buoyancy: weight of displaced fluid.
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Average acceleration
a_avg = Δv / Δt.
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Average velocity
v_avg = Δx / Δt along one axis.
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Bernoulli (horizontal flow)
P + ½ρv² constant along a streamline; solve P₂ or v₂.
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Binding energy (mass defect)
ΔE = Δm c² with Δm in kg.
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Biot–Savart (circular loop, center)
B = μ₀ I / (2R) at the center of a circular loop.
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Blackbody radiation
Wien peak wavelength or Stefan–Boltzmann exitance.
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Bulk modulus
B ≈ −ΔP / (ΔV/V).
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Buoyant force
F_b = ρ_fluid V_displaced g.
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Capacitance from Q and V
C = |Q|/|V|.
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Carnot efficiency
η = 1 − Tc/Th with temperatures in kelvin.
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Center of mass (two particles, 1D)
x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂).
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Circuit simulator (lite)
Ideal DC series: current and resistor voltages from V, R₁, R₂.
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Collision (1D)
Elastic v₁′, v₂′ or perfectly inelastic common speed.
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Coulomb’s law
Force magnitude between two point charges in SI.
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Critical angle
sin θ_c = n₂/n₁ when n₁ > n₂.
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De Broglie wavelength
λ = h/p with p = mv.
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Density
ρ = m/V.
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Dimensional analysis (speed)
km/h ↔ m/s using exact factor 1/3.6.
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Displacement (constant a)
s = ut + ½at².
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Distance (uniform speed)
Distance ≈ |v| t when speed is constant on a straight path.
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Doppler effect (sound)
Classic 1D cases for source or observer motion.
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Echo time
Round-trip time t = 2d/v.
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Efficiency
η = (useful output / total input) × 100%.
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Efficiency (systems)
η = (useful output / total input) × 100%.
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Elastic / inelastic collision solver
Same 1D solver with mode selection.
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Electric current from charge
Average I = ΔQ/Δt.
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Electric field (point charge)
|E| = k|Q|/r².
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Electric potential (point charge)
V = kQ/r with V(∞) = 0.
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Electrical energy
E = Pt or E = VIt.
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Energy conversion (percent efficiency)
E_out = η E_in with η as a percent.
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Energy converter
J, eV, kcal, and other energy units.
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Error calculation
Absolute, relative, and percent error from measured and accepted values.
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Escape velocity
v_esc = √(2GM/r) from a spherical body.
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Exam time management planner
Split total time across questions with a review buffer.
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Experimental data analyzer
Mean, sample standard deviation, and SEM from a list of numbers.
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Faraday’s law (average EMF magnitude)
|ε|_avg = N |ΔΦ/Δt|.
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Field line visualizer (lite)
Qualitative radial field circles for a point charge.
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Force (F = ma)
Net force magnitude from mass and acceleration.
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Force converter
N, kN, dyn, lbf.
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Frequency converter
Hz, kHz, MHz, rpm, rad/s (via ω/2π).
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Frequency from period
f = 1/T.
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g from M and r
g = GM/r² outside a spherically symmetric mass.
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Graph plotter (x–y)
Paste x,y pairs; draw a connected line in the browser (SVG).
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Gravitational force
Newton’s law F = G m₁ m₂ / r² in SI.
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Gravitational potential energy
PE = mgh near Earth.
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Half-life and decay constant
T½ = ln 2 / λ and λ = ln 2 / T½.
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Hall effect
Hall voltage V_H = B I / (n e t) for one carrier.
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Heat conduction (slab)
Steady power P = kAΔT/d through a flat slab.
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Heat engine efficiency
η = 1 − Qc/Qh from heat exchanges.
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Ideal gas law (physics)
PV = nRT with P (atm), V (L), T (K).
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Impulse
J = F Δt.
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Inclined plane acceleration
a = g(sin θ − μ cos θ) down the slope.
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Induced EMF (motional)
ε = B ℓ v with B, ℓ, v mutually perpendicular.
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JEE physics score (illustrative)
Rough raw score with +4/−1 style inputs — not official.
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Kinetic energy
KE = ½ m v².
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Kinetic friction
f = μ N for kinetic friction magnitude.
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Kirchhoff (simple circuits)
Series KVL loop or two-branch parallel across an EMF.
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Lab measurement error
Absolute, relative, and percent error vs an accepted value.
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Least count (vernier-style)
LC = (smallest main-scale division) / n vernier divisions.
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Linear magnification
m = −v/u (Cartesian).
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Linear thermal expansion
ΔL = α L₀ ΔT.
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Lorentz force (magnetic part)
F = |q| v B sin θ (B contribution only).
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Magnetic field (long straight wire)
B = μ₀ I / (2πr) at perpendicular distance r.
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Mass–energy (E = mc²)
Rest energy in joules and MeV.
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Mechanical energy
E = KE + PE (scalar sum for this tool).
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Mechanical work (two-stage sum)
W_total = F₁d₁ + F₂d₂ with θ = 0.
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Moment of inertia
Standard formulas: point, hoop, disk, sphere, rod.
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Momentum
p = mv.
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Motion graph visualizer
Sketch x(t)=ut+½at² for chosen u, a, and t range.
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NEET physics score (illustrative)
Same illustrative negative-marking helper for physics MCQs.
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Net force (1D)
Sum three signed force components on one axis.
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Normal force
Flat surface N = mg; incline N = mg cos θ.
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Nuclear decay (exponential)
N = N₀ e^(−λt) with λ from half-life.
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Ohm’s law
Solve V = IR for V, I, or R.
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Optical power (diopters)
P = 1/f with f in meters.
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Optics ray diagram (lite)
Thin-lens v, m, and a two-ray schematic from u, f, h.
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Orbital speed (circular)
v = √(GM/r) for a circular orbit.
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Parallel resistors (two)
Two-branch equivalent resistance.
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Parallel-plate capacitor
C = ε₀ εᵣ A / d.
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Pendulum period
T = 2π√(L/g) small-angle approximation.
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Percentage error
Percent error from measured and accepted values.
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Period from frequency
T = 1/f.
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Photoelectric effect
K_max = hf − φ with φ in eV.
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Physics attempt analyzer
Accuracy and rough score from correct/wrong/skipped counts.
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Physics unit converter
Convert length, mass, time, speed, force, and energy via SI base factors.
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Planck equation (E = hf)
Photon energy from frequency.
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Power
P = W/t or P = F v cos θ.
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Power consumption
P = V I or P = E/t.
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Power in a circuit
P = IV, I²R, or V²/R.
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Pressure (fluid, from force)
P = F/A.
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Pressure converter
Pa, atm, bar, mmHg, psi.
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Projectile max height
H = (v₀ sin θ)² / (2g) above launch height.
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Projectile position
x(t), y(t) from v₀ and θ; no air resistance.
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Projectile range
Range on level ground: R = v₀² sin(2θ) / g.
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Projectile time of flight
T = 2 v₀ sin θ / g back to launch height.
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Quantum energy levels
Hydrogen-like Bohr energies or particle-in-a-box levels.
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Rank predictor (toy)
Toy rank from an assumed percentile — not a real predictor.
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Refraction (Snell’s law)
Same as Snell’s law: n₁ sin θ₁ = n₂ sin θ₂.
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Relative velocity (1D)
v_AB = v_A − v_B on one axis.
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Resistance
R = V/I or R = ρL/A.
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Resonance (string / pipe)
String fundamental or open–open / closed–open pipe harmonics.
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Rolling motion energy
Total KE = ½mv² + ½Iω² with ω = v/R.
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Rotational kinetic energy
K = ½ I ω².
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Satellite motion (circular)
Period, speed, and angular speed for a circular orbit.
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Scientific notation
Write a number as m × 10^n with 1 ≤ |m| < 10.
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Semiconductor thermal scale
kT in eV and E_g/(kT) for order-of-magnitude reasoning.
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Series resistors
R_total = R₁ + R₂ (+ optional R₃).
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Shear modulus
G = τ/γ.
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Significant figures
Round a value to n significant figures.
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Simple harmonic motion
ω = √(k/m), T, f, and optional x = A cos(ωt).
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Snell’s law
n₁ sin θ₁ = n₂ sin θ₂; solve θ₂, θ₁, n₂, or n₁.
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Sound intensity and level
β = 10 log₁₀(I/I₀) with I₀ = 10⁻¹² W/m².
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Sound intensity level (dB)
β = 10 log₁₀(I/I₀), I₀ = 10⁻¹² W/m².
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Special relativity calculator
γ, contracted length, and dilated time from v and rest values.
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Specific heat (Q = mcΔT)
Heat for a temperature change.
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Speed converter
m/s, km/h, mph, and other speed units.
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Speed of sound in air (approx.)
v ≈ 331.3 + 0.606 T_C m/s.
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Spherical mirror formula
Same 1/f = 1/v + 1/u form with Cartesian signs.
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Strain
ε = ΔL/L₀.
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Stress
σ = F/A.
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SUVAT solver
Fill three of u, v, a, s, t; get the rest for constant acceleration.
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Temperature converter
Kelvin, °C, and °F with exact offsets.
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Tension (Atwood machine)
Ideal string and pulley: a and T from m₁, m₂.
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Thin lens formula
1/f = 1/v + 1/u; solve for f, u, or v (SI meters).
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Time from u, v, a
t = (v − u) / a when acceleration is non-zero.
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Torque
τ = r F sin θ.
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Uncertainty calculator
Combine independent uncertainties for sum or product.
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Viscosity (Poiseuille flow)
Q = π r⁴ ΔP / (8 η L) for laminar pipe flow.
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Volume flow rate
Q = A v.
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Wave simulation (snapshot)
Sine snapshot y ∝ sin(kx + φ) with adjustable λ and φ.
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Wave speed
v = f λ.
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Work (constant force)
W = F d cos θ.
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Young’s modulus
E = σ/ε.
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