IGCSE Physics Formula List: Motion, Forces, Energy

Cambridge IGCSE Physics (CIE 0625 and the newer 0972 edition) does not give candidates a printed formula booklet at the front of the paper. The only equations you see on the page are the ones the syllabus flags as given, and for motion, forces and energy almost every single equation must be recalled from memory. That rule applies to both Core and Extended tiers, in Paper 2, Paper 3 and Paper 4.

The good news is that the recall list is shorter than students think. Three blocks of formulas carry about 80 percent of the calculation marks across the calculation papers: kinematics, Newton mechanics, and work, energy and power. Master these and you can attack any direct calculation, any rearrangement question and most of the multi step problems that show up in the longer structured items.

This guide gives you the full working list, written exactly the way the official mark schemes write it, with units, the tier (Core or Extended) and the typical exam context. Use it as a memorisation target, not as a reading list. Close the book, take a blank sheet of paper, and try to reproduce each block from scratch. By the week of the exam, you should be able to write the whole table in under three minutes.

For exam day timing and paper structure across the whole subject, see the [IGCSE Physics exam guide](/igcse-physics-exam-guide). For the wider catalogue covering electricity, waves and thermal physics formulas too, the [IGCSE Physics formulas explained](/igcse-physics-formulas-explained) article is your next stop.

These appear on essentially every Paper 3 and Paper 4 in some form, usually attached to a velocity time graph or a moving vehicle scenario.

• Speed: v = d / t. Units metres per second (m/s). Use total distance over total time when the question asks for average speed. - Acceleration: a = (v minus u) / t. Units metres per second squared (m/s²). A negative value means deceleration, and you must keep the sign through to the answer. - Distance from a velocity time graph: distance equals the area under the line. For a triangular section that is one half base times height. For a trapezium, add the two parallel sides, multiply by the horizontal width, divide by two. - Extended only, the SUVAT relation: v² = u² + 2 a s. This unlocks problems where time is not given, for example a braking car where you know initial speed, deceleration and stopping distance.

Worked micro example.

A car accelerates from 5 m/s to 25 m/s in 4 seconds. Acceleration is (25 minus 5) divided by 4, which gives 5 m/s². Distance is average speed times time, so (5 plus 25) divided by 2, times 4, equals 60 m. Notice we did not need v² = u² + 2 a s because time was given.

The single biggest trap in kinematics is swapping u and v. The convention is u for initial velocity, v for final velocity. Before starting any algebra, write u =, v =, a =, t =, s = on the side of the page and fill in the values from the question. This one habit removes most kinematics errors in mock papers.

This block carries the most marks because forces tie into motion, into pressure, into density and into turning effects.

• Newton's second law: F = m a. Units newtons (N). F is the resultant force, never an individual push or pull. - Weight: W = m g. On Earth, g is taken as 9.8 N/kg in the latest CIE mark schemes, although 10 N/kg is accepted in many older papers and in some Core questions. Always check the data on page two of the exam paper. - Density: ρ = m / V. Units kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³). Convert carefully. - Pressure (solids): p = F / A. Units pascals (Pa), where 1 Pa equals 1 N/m². - Pressure in a liquid (Extended): Δp = ρ g Δh. Used for submarines, dams, manometers and U tube problems. - Moment of a force: moment = F × d, where d is the perpendicular distance from the pivot to the line of action. Units newton metres (N m). Apply the principle of moments: clockwise equals anticlockwise in equilibrium. - Hooke's law (Extended): F = k x, where k is the spring constant (N/m) and x is the extension from natural length.

The most common mark scheme penalty on F = m a is forgetting that F is the resultant. If a 2 kg object is pulled with 10 N forward and 4 N friction acts backwards, the resultant is 6 N, so acceleration is 3 m/s², not 5. Always draw a free body diagram or at least write the forces with signs before substituting.

For a deeper run through moments, equilibrium and Newton's three laws with diagrams, see the [IGCSE Physics forces and motion complete guide](/igcse-physics-forces-motion-complete-guide).

These three are different physical quantities but the syllabus groups them together, partly because they share units (joules and watts) and partly because they almost always appear together in energy transfer questions.

• Work done: W = F d, where d is the distance moved in the direction of the force. Units joules (J). - Kinetic energy: KE = ½ m v². Units joules. Watch the squaring: doubling the speed quadruples the KE. - Gravitational potential energy change: ΔGPE = m g Δh. Units joules. Use the change in height, not the absolute height above the ground. - Power: P = E / t = W / t. Units watts (W), where 1 W equals 1 J/s. - Efficiency: efficiency = useful energy out / total energy in, multiplied by 100 if you want a percentage. Always less than 1 (or less than 100 percent) in real systems.

Work and energy share the same units because, in the simplest case, the work done on an object becomes its energy. When a student writes 'the work done by the engine equals the kinetic energy gained' they are not making things up, they are applying conservation of energy. In Paper 4 questions this is often the only clean route to a final speed when forces are messy.

A frequent slip on efficiency is forgetting to include the wasted energy in the denominator. Total energy in equals useful energy out plus the energy lost as heat, sound, or anything else. Mark schemes are very strict about this.

This is the kind of question that lands in Paper 4 Extended, usually worth six or seven marks split across parts.

Question.

A 1200 kg car accelerates from rest along a flat road. The engine provides a constant driving force of 3600 N. The total resistive force (friction plus air resistance) is 600 N. After 10 seconds, find: (a) the acceleration (b) the speed at t = 10 s (c) the distance travelled (d) the kinetic energy at t = 10 s (e) the useful power developed by the engine, averaged over the 10 seconds.

Step 1, resultant force.

F resultant = 3600 minus 600 = 3000 N.

Step 2, acceleration.

a = F / m = 3000 / 1200 = 2.5 m/s².

Step 3, speed at t = 10 s.

v = u + a t = 0 + 2.5 × 10 = 25 m/s.

Step 4, distance.

s = u t + ½ a t² = 0 + ½ × 2.5 × 100 = 125 m. You can confirm this with the velocity time graph area, ½ × 10 × 25, which also equals 125 m.

Step 5, kinetic energy.

KE = ½ m v² = ½ × 1200 × 25² = ½ × 1200 × 625 = 375 000 J or 375 kJ.

Step 6, useful power.

Useful work done by the engine equals driving force times distance, so 3600 × 125 = 450 000 J. Average power = 450 000 / 10 = 45 000 W or 45 kW.

That single question touches every formula in this guide. Notice how the mark scheme rewards method marks for clean substitution even when arithmetic slips: always write equation, substitution, evaluation on three separate lines per part. Examiners can then award the method marks even if the final number is wrong.

For a long list of common slips on exactly this kind of multi part problem, the [IGCSE Physics calculations students get wrong](/igcse-physics-calculations-students-get-wrong) article shows mark losing mistakes alongside the correct working.

Memorising is not the same as understanding, but in IGCSE Physics you need both. Three techniques work much better than rereading the textbook.

• Closed book recall sprints. Once a week, on a blank sheet of paper, write the entire equation list with units and the tier (Core or Extended). Time yourself. Aim for under three minutes by the week of the exam. The act of recall, not rereading, is what builds long term memory. - One formula per question. Take any past paper question on motion, forces or energy and circle the single equation that unlocks it. Often it is exactly one, sometimes two. This trains the diagnostic step that examiners reward in the longer structured questions. - Unit checks at every line. Before writing the final number, write the units on the right hand side and the left hand side of the equation. If they do not match (for example, you get m/s when the answer should be m/s²) the formula is wrong. This habit alone catches roughly half of all algebra errors students make under exam pressure.

A realistic three week revision rotation looks like this. Week one, drill formula recall and one mark substitution questions. Week two, multi part Paper 4 questions under timed conditions. Week three, full past papers under exam timing. End each session with one timed past paper question and mark it yourself against the official scheme.

If you can write the formulas in under three minutes and apply them inside a five mark structured question in under four minutes, you are at A star pace.