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Physics Formula Solver
Solve 20+ physics formulas for any variable with step-by-step solutions. Select a formula, choose which variable to calculate, enter the known values, and see the result with the rearranged equation and substitution. Covers mechanics, energy, waves and electricity in SI units.
How to Use the Physics Formula Solver
Select a physics category (Mechanics, Energy, Waves or Electricity), choose a formula, then pick which variable to solve for. Enter the known values and click Calculate. Furthermore, the solver shows the rearranged formula and step-by-step substitution alongside the result. Additionally, copy the full solution for homework or lab reports.
- Select a categoryChoose from Mechanics, Energy and Work, Waves, or Electricity.
- Choose a formulaPick from 20+ physics formulas in the dropdown.
- Select what to solveChoose which variable to calculate. Input fields update accordingly.
- Enter known valuesFill in the known quantities in SI units.
- View the solutionSee the result with formula, rearranged form, substitution and units.
Mechanics Formulas
Mechanics is the branch of physics dealing with motion and forces. The formulas in this category cover kinematics (describing motion) and dynamics (explaining why objects move). Furthermore, these formulas form the foundation of classical mechanics established by Isaac Newton in his Principia Mathematica (1687).
| Formula | Equation | Variables | SI units |
|---|---|---|---|
| Velocity | v = d / t | velocity, distance, time | m/s, m, s |
| Acceleration | a = (v₂ − v₁) / t | acceleration, velocities, time | m/s², m/s, s |
| Newton's 2nd Law | F = ma | force, mass, acceleration | N, kg, m/s² |
| Weight | W = mg | weight, mass, gravity | N, kg, m/s² |
| Momentum | p = mv | momentum, mass, velocity | kg·m/s, kg, m/s |
| Impulse | J = FΔt | impulse, force, time | N·s, N, s |
| Kinematic | v² = v₀² + 2as | velocities, acceleration, displacement | m/s, m/s², m |
Energy and Work Formulas
Energy is the capacity to do work. The energy formulas in this tool cover kinetic energy (energy of motion), potential energy (energy of position), mechanical work and power. Furthermore, the principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another.
| Formula | Equation | Variables | SI units |
|---|---|---|---|
| Kinetic Energy | KE = ½mv² | kinetic energy, mass, velocity | J, kg, m/s |
| Potential Energy | PE = mgh | potential energy, mass, gravity, height | J, kg, m/s², m |
| Work | W = Fd | work, force, distance | J, N, m |
| Power | P = W/t | power, work, time | W, J, s |
| Efficiency | η = W_out/W_in | efficiency, output, input | %, J, J |
Wave and Oscillation Formulas
Waves transfer energy through oscillations without transferring matter. The wave formulas cover the relationship between speed, frequency and wavelength. Furthermore, the pendulum formula describes simple harmonic motion, one of the most fundamental oscillatory systems in physics. Snell's Law describes refraction of waves at material boundaries.
| Formula | Equation | Variables |
|---|---|---|
| Wave Speed | v = fλ | speed, frequency, wavelength |
| Period and Frequency | f = 1/T | frequency, period |
| Pendulum Period | T = 2π√(L/g) | period, length, gravity |
| Snell's Law | n₁sinθ₁ = n₂sinθ₂ | refractive indices, angles |
Electricity Formulas
Electricity formulas describe the behaviour of electric charge, current and electromagnetic fields. Ohm's Law is the most fundamental relationship in circuit analysis. Furthermore, Coulomb's Law describes the electrostatic force between charged particles, analogous to Newton's law of gravitation for masses.
| Formula | Equation | Variables |
|---|---|---|
| Ohm's Law | V = IR | voltage, current, resistance |
| Electrical Power | P = VI | power, voltage, current |
| Coulomb's Law | F = kQ₁Q₂/r² | force, charges, distance |
| Electrical Energy | E = Pt | energy, power, time |
Solving for Any Variable
Every formula in this tool can be rearranged to solve for any variable it contains. Select the target variable from the dropdown and the tool automatically rearranges the equation. Furthermore, the step-by-step output shows the original formula, the rearranged form, the substitution of known values and the final result with units.
SI Units Reference
All calculations in this tool use the International System of Units (SI). Using consistent SI units ensures dimensional correctness and prevents unit-conversion errors. Furthermore, the seven SI base units (metre, kilogram, second, ampere, kelvin, mole and candela) form the foundation for all derived units like newtons, joules, watts and ohms.
| Quantity | SI unit | Symbol | Derived from |
|---|---|---|---|
| Force | Newton | N | kg·m/s² |
| Energy / Work | Joule | J | N·m = kg·m²/s² |
| Power | Watt | W | J/s = kg·m²/s³ |
| Voltage | Volt | V | W/A = kg·m²/(A·s³) |
| Resistance | Ohm | Ω | V/A |
| Frequency | Hertz | Hz | 1/s |
| Momentum | — | kg·m/s | kg·m/s |
| Charge | Coulomb | C | A·s |
Tips for Physics Problem Solving
Identify the known and unknown quantities first. Write down every value given in the problem with its unit. Furthermore, select the formula that contains both the known values and the unknown you need to find. If no single formula works, you may need to use two formulas in sequence.
Always check your units. If you mix metres with kilometres or seconds with hours, the result will be wrong. Convert all values to SI units before substituting into formulas. Furthermore, check whether the result makes physical sense. A car cannot have negative mass. A velocity cannot exceed the speed of light for everyday objects.
Newton's Laws of Motion
Newton's three laws of motion form the foundation of classical mechanics. The first law (inertia) states that an object remains at rest or in uniform motion unless acted upon by a net force. Furthermore, the second law (F = ma) quantifies how force, mass and acceleration are related. The third law states that every action has an equal and opposite reaction.
The second law is the most computationally useful. It connects force to measurable quantities (mass and acceleration). Furthermore, weight is a special case where the acceleration equals gravitational acceleration (g = 9.81 m/s² on Earth). Momentum (p = mv) and impulse (J = FΔt) are direct consequences of the second law applied over time.
Conservation Laws in Physics
Conservation laws are among the most powerful principles in physics. Conservation of energy states that total energy in a closed system remains constant. Furthermore, conservation of momentum states that total momentum is conserved in the absence of external forces. These laws allow you to solve problems where forces are unknown or difficult to measure.
In an elastic collision, both kinetic energy and momentum are conserved. In an inelastic collision, momentum is conserved but kinetic energy is not. Furthermore, the work-energy theorem states that the net work done on an object equals its change in kinetic energy. This connects the work formula (W = Fd) to the kinetic energy formula (KE = ½mv²).
Worked Example: Projectile Motion
A ball is thrown horizontally from a 20-metre cliff at 15 m/s. To find how long it takes to hit the ground, use the kinematic equation with vertical motion: h = ½gt². Rearranging gives t = √(2h/g) = √(2 × 20 / 9.81) = √(4.077) = 2.02 seconds. Furthermore, the horizontal distance is d = v × t = 15 × 2.02 = 30.3 metres.
Worked Example: Circuit Analysis
A circuit has a 12V battery connected to a 4Ω resistor. Using Ohm's Law (I = V/R), the current is 12/4 = 3 amperes. Furthermore, the power dissipated is P = VI = 12 × 3 = 36 watts. The energy consumed in 60 seconds is E = Pt = 36 × 60 = 2,160 joules.
For resistors in series, total resistance is R_total = R₁ + R₂. For resistors in parallel, 1/R_total = 1/R₁ + 1/R₂. Furthermore, Kirchhoff's voltage law states that the sum of all voltages around a closed loop equals zero. These principles allow analysis of complex circuits using the basic formulas in this tool.
Physics in Everyday Life
Physics formulas describe everyday phenomena. Car braking distances depend on the kinematic equation v² = v₀² + 2as, where deceleration (negative a) and initial speed determine stopping distance. Furthermore, doubling your speed quadruples the braking distance because kinetic energy scales with velocity squared.
Household electricity follows Ohm's Law. A 100W light bulb connected to 220V mains draws I = P/V = 100/220 = 0.45 amperes. Furthermore, pendulum clocks use the period formula T = 2π√(L/g) to maintain accurate timekeeping. A 1-metre pendulum has a period of approximately 2 seconds, which is why grandfather clocks use pendulums close to this length.