This physics equations explained guide shows what common formulas mean, when they apply, how to check their units, and how to rearrange them without relying on memorisation alone. Use it as a working physics formula sheet for homework, revision, and exam preparation.
Overview
A physics equation is more than a collection of letters. Each symbol represents a measurable quantity, the units tell you how those quantities relate, and the conditions of the equation determine when it is valid. A reliable approach is therefore:
- Identify the physical situation and the quantities provided.
- Choose an equation that includes the unknown and the known values.
- Convert all values into compatible units.
- Rearrange the equation before substituting if that makes the unknown clearer.
- Calculate, include the correct unit, and check whether the result is sensible.
Formula triangles can help with simple relationships, but they are a memory aid rather than a replacement for understanding. For equations with powers, several terms, or special conditions, algebra is safer than a triangle.
Read symbols and units carefully
Common symbols can have different meanings in different topics. For example, v may represent velocity, while V often represents voltage or volume. Capital letters and lower-case letters matter. Before calculating, write a short list such as known: distance = 120 m; time = 10 s; unknown: speed.
Use SI units unless your question or course specifies otherwise: metres for distance, seconds for time, kilograms for mass, amperes for current, volts for potential difference, and joules for energy. Unit conversions should happen before substitution, not after the calculator has produced an answer.
Step-by-step workflow
1. Motion and kinematics
Speed or average velocity: v = d / t. Here, v is speed or average velocity, d is distance or displacement, and t is time. Use it when the question relates a distance travelled to a time interval. Rearrange it as d = vt or t = d / v.
Acceleration: a = (v - u) / t, where u is initial velocity and v is final velocity. Use this when velocity changes over a measured time. Rearranging gives v = u + at. The equation assumes the acceleration is constant over the interval.
For constant-acceleration problems, other useful relationships include s = ut + 1/2 at² and v² = u² + 2as. Choose the equation that contains the quantities you know and the quantity you need. The second equation is especially useful when time is not given. In these equations, s is displacement, not always total distance, and velocities should include their direction where appropriate.
2. Forces and momentum
Newton’s second law: F = ma. Force is measured in newtons, mass in kilograms, and acceleration in metres per second squared. Rearrange it as m = F / a or a = F / m. Use the net or resultant force when several forces act on an object. A force diagram can help you decide which forces should be included.
Weight: W = mg, where m is mass and g is gravitational field strength. Near Earth’s surface, a course may use a value close to 9.8 N/kg or another stated value. Do not confuse mass, measured in kilograms, with weight, measured in newtons.
Momentum: p = mv. Momentum depends on both mass and velocity, so direction matters. Its unit is kilogram metres per second. Use momentum equations for collisions, recoil, and changes in motion, while checking whether the question treats the system as isolated.
3. Work, energy, and power
Work done: W = Fd when the force acts in the direction of the movement. Work and energy are measured in joules. If the force is at an angle, the component of force in the direction of movement is the relevant part, so do not apply the simple form automatically.
Kinetic energy: Eₖ = 1/2 mv². This is the energy of motion. Because velocity is squared, doubling speed changes kinetic energy by a factor of four when mass stays the same.
Gravitational potential energy: Eₚ = mgh. Use it for changes in height in a nearly uniform gravitational field. The height should be measured relative to a clearly chosen reference level. Power: P = E / t, so energy transferred per unit time is measured in watts. Rearrange it as E = Pt or t = E / P.
4. Electricity
Charge, current, and time: Q = It. Charge Q is measured in coulombs, current I in amperes, and time t in seconds. Rearrange it as I = Q / t or t = Q / I.
Potential difference: V = IR, commonly called Ohm’s law. Voltage is measured in volts, current in amperes, and resistance in ohms. Rearrange it as I = V / R or R = V / I. Check whether the component behaves in a way that allows this relationship to be used; some components do not have constant resistance.
Electrical power: P = VI. Combining this with Ohm’s law gives P = I²R and P = V² / R. Select the version that uses the values provided. Electrical energy can then be found with E = Pt, provided power and time use compatible units.
5. Waves and thermal physics
Wave speed: v = fλ, where f is frequency and λ is wavelength. Frequency is measured in hertz and wavelength in metres. Rearrange it as f = v / λ or λ = v / f. Make sure the wavelength is measured between matching points on adjacent waves, such as crest to crest.
Density: ρ = m / V. Density is mass per unit volume. Rearrange it as m = ρV or V = m / ρ. Common mistakes include using cubic centimetres with kilograms per cubic metre without converting the volume.
Thermal energy change: ΔE = mcΔT. Use this when a material changes temperature without a change of state. The specific heat capacity, c, describes the energy needed to raise a unit mass by one degree. For a change of state, a latent-heat equation such as E = mL may be more appropriate. Check what the question says before choosing.
6. Rearrange equations with algebra
To rearrange an equation, perform the same operation on both sides. For example, begin with P = E / t. Multiply both sides by t to obtain Pt = E, which can be written as E = Pt. To make t the subject, divide both sides by P: t = E / P.
For an equation such as Eₖ = 1/2 mv², first multiply by 2: 2Eₖ = mv². Divide by m: 2Eₖ / m = v². Finally take the square root: v = √(2Eₖ / m). Keeping each step visible reduces sign, fraction, and square-root errors.
Tools and handoffs
A useful physics formula sheet should have four columns: equation, meaning of each symbol, SI units, and conditions or reminders. Add one short example only after you can explain when the equation applies. This keeps the sheet useful for retrieval practice rather than turning it into a crowded wall of formulas.
Use a calculator for arithmetic, but do the setup by hand. A calculator cannot identify whether you needed displacement rather than distance or whether minutes should be converted to seconds. A unit-conversion table, a ruler for reading graphs, and a clearly labelled force diagram are often more useful than additional formulas.
For multi-step questions, connect the equations rather than searching for one formula that contains every number. For example, a force question may require acceleration first, followed by F = ma. If you need a fuller method for interpreting a written problem, see How to Solve Physics Word Problems. For broader revision planning, use the Science Exam Revision Planner.
Quality checks
- Units: Do the units match the equation, and is the final unit appropriate for the quantity?
- Sign and direction: Could the value be negative because of a chosen direction, or should it be a positive magnitude?
- Conditions: Does the formula require constant acceleration, a uniform field, a particular circuit behaviour, or no change of state?
- Magnitude: Is the answer roughly plausible compared with the values in the question?
- Rounding: Have you kept extra digits during working and rounded only at the end, according to your course guidance?
After solving, cover the formula and explain the choice aloud in one sentence. For example: I used wave speed equals frequency multiplied by wavelength because frequency and wavelength are given and speed is required. This is a fast self-test that checks understanding, not just substitution.
When to revisit
Return to this physics study guide whenever your class begins a new unit, your formula sheet changes, or you notice the same type of error in practice questions. Keep a short error log with three entries: the question type, the mistake, and the check that would have caught it. Review that log before homework and again before a test.
For an action-focused revision session, choose five equations from one topic. For each one, write what every symbol means, state the units, rearrange it for one different variable, and complete one short question without looking at the formula. Finish by marking which equations still feel uncertain. Those become the next day’s retrieval practice, while secure equations can be revisited later. This cycle turns a static physics formula sheet into a working system for homework help and exam preparation.
