Functions of the Skeleton
Support, protection (skull, ribs), movement (attachment for muscles), shape, blood cell production (red marrow), mineral storage (calcium, phosphorus). Cambridge IGCSE Physical Education 0413
🏃 Cambridge IGCSE Physical Education Formula Sheet 2026
Everything Cambridge IGCSE PE students need — anatomy & physiology, movement analysis, energy systems, fitness components and training, with all the key calculations in one place.
Anatomy & Physiology Movement Analysis Energy Systems Training & Calculations
Our formula sheets are free to download — save this one as PDF for offline revision.
Aligned with the latest 2026 syllabus and board specifications. This sheet is prepared to match your exam board’s official specifications for the 2026 exam series.
All the Theory and Calculations for IGCSE PE in One Sheet
Cambridge IGCSE Physical Education (0413) blends theory with practical performance. This formula sheet pulls together the anatomy and physiology you need to label and explain, the movement analysis frameworks (planes, axes, levers), energy systems, components of fitness with named tests, training principles, and every calculation that examiners expect — heart rate, cardiac output, BMI and more.
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Skeletal, muscular, cardiovascular and respiratory systems summarised
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Planes, axes and lever systems with sporting examples
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Aerobic vs anaerobic energy systems and EPOC
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All key formulas — Max HR, target zones, cardiac output, BMI
Skeletal & Muscular Systems
Functions, joint types and muscle pairs you must be able to identify.
Joint Types & Movement
Ball-and-socket
Shoulder, hip — flexion, extension, abduction, adduction, rotation, circumduction Hinge
Elbow, knee, ankle — flexion and extension only Pivot
Neck (atlas/axis) — rotation Gliding
Carpals (wrist) — small sliding movements Saddle
Thumb (carpometacarpal) — flexion, extension, abduction, adduction Condyloid
Wrist — flexion, extension, abduction, adduction Antagonistic Muscle Pairs
Agonist contracts; antagonist relaxes.
Upper arm
Biceps (agonist in flexion) ↔ Triceps (agonist in extension) Upper leg
Quadriceps (extension at knee) ↔ Hamstrings (flexion at knee) Hip
Gluteals (extension) ↔ Hip flexors (flexion) Muscle Fibre Types
Slow-twitch (Type I)
Aerobic, fatigue-resistant — endurance events (marathon) Fast-twitch (Type II)
Anaerobic, powerful, fatigue quickly — sprinting, weightlifting Cardiovascular & Respiratory Systems
Key calculations and gas-exchange concepts.
Heart Rate (HR)
From R-R interval
HR (bpm) = 60 ÷ R-R interval in seconds Resting HR
Typically 60–80 bpm; lower in trained athletes (bradycardia) Stroke Volume & Cardiac Output
Stroke volume (SV)
Volume of blood ejected from the left ventricle per beat (ml) Cardiac output (Q)
Q = HR × SV (l/min) Training increases SV → resting HR drops while Q is maintained.
Respiratory Volumes
Tidal volume (TV)
Volume of air inhaled/exhaled in a normal breath (~0.5 l) Vital capacity
Maximum air exhaled after maximum inhalation (~4.5–5 l in adults) Minute ventilation
VE = TV × breathing rate Gaseous Exchange
Occurs at the alveoli by diffusion: O₂ moves from alveoli → blood; CO₂ moves from blood → alveoli. Large surface area, thin walls, moist lining and rich capillary network maximise diffusion. Movement Analysis — Planes, Axes & Levers
Identify movements using the correct plane/axis pairing.
Planes of Movement
Sagittal
Divides body left/right — flexion, extension (e.g. running, biceps curl) Frontal
Divides body front/back — abduction, adduction (e.g. star jump, cartwheel) Transverse
Divides body top/bottom — rotation (e.g. discus throw) Axes of Rotation
Transverse (mediolateral)
Pairs with sagittal plane — somersault Sagittal (anteroposterior)
Pairs with frontal plane — cartwheel Vertical (longitudinal)
Pairs with transverse plane — pirouette Lever Systems
1st-class
Fulcrum between effort and load — neck nodding (atlas/skull) 2nd-class
Load between fulcrum and effort — calf raise (mechanical advantage) 3rd-class
Effort between fulcrum and load — biceps curl (most levers in the body) Mechanical advantage = effort arm ÷ load arm. 2nd-class levers have MA > 1.
Energy Systems
Aerobic and anaerobic pathways for ATP production.
Aerobic vs Anaerobic
Aerobic
Glucose + O₂ → CO₂ + H₂O + ATP — long, low-intensity (marathon) Anaerobic — ATP-PC
Phosphocreatine → ATP — 0–10 seconds, max-intensity (100 m sprint, jump) Anaerobic — lactic acid
Glucose → lactic acid + ATP — ~10 s to 2 min, high-intensity (400 m) EPOC (Excess Post-exercise Oxygen Consumption)
Extra O₂ taken in after exercise to repay the O₂ deficit, remove lactic acid, restore phosphocreatine and replenish myoglobin stores. Sometimes called 'oxygen debt'. Components of Fitness & Tests
Each component pairs with a recognised test.
Health-Related Components
Cardiovascular endurance
Cooper 12-minute run / Multi-stage fitness test Muscular endurance
1-minute sit-up or press-up test Strength
1RM (one-rep max) test Flexibility
Sit-and-reach test Body composition
BMI, skinfold callipers, bioelectrical impedance Skill-Related Components
Speed
30 m sprint test Power
Vertical jump (Sargent) test Agility
Illinois agility run Balance
Stork stand test Reaction time
Ruler drop test Coordination
Alternate-hand wall-toss test Training Principles & Methods
SPORT and FITT — plus the main training methods.
SPORT Principles
S
Specificity — training matches the demands of the sport P
Progression — gradually increase demand O
Overload — work harder than normal R
Reversibility — fitness is lost if training stops T
Tedium — vary training to maintain motivation FITT Principles for Overload
F
Frequency — how often I
Intensity — how hard T
Time — how long T
Type — what kind of training Methods of Training
Continuous
Steady, low-intensity — improves aerobic endurance Fartlek
'Speed play' — variable pace, mixes aerobic & anaerobic Interval
Periods of work & rest — improves both energy systems Circuit
Stations targeting different muscles/components Weight
Resistance — sets, reps, %1RM for strength/endurance/power Plyometric
Bounding, depth jumps — develops power HIIT
Short maximal bursts with brief recovery — anaerobic + aerobic gains Key Calculations
The numerical formulas examiners expect you to recall.
Heart Rate Formulas
Maximum HR
Max HR = 220 − age (bpm) Aerobic target zone
60–80% of Max HR Anaerobic target zone
80–90% of Max HR Cardiac Output
Q
Q = HR × SV Body Mass Index
BMI
BMI = weight (kg) ÷ height² (m²) Underweight <18.5 | Normal 18.5–24.9 | Overweight 25–29.9 | Obese ≥ 30.
Worked Example
Athlete aged 16, HR 180 bpm, SV 100 ml. Max HR = 220 − 16 = 204 bpm. % Max HR = 180 ÷ 204 ≈ 88% (anaerobic zone). Q = 180 × 100 = 18,000 ml/min = 18 l/min. Skill Acquisition, Feedback & Information Processing
Coaching theory examiners commonly assess.
Skill Classification Continua
Open ↔ Closed
Open — environment changes (football pass); closed — predictable (free throw) Gross ↔ Fine
Gross — large muscle groups (sprint); fine — small precise (darts) Basic ↔ Complex
Decision-making demand Self-paced ↔ Externally paced
Who controls the timing Information Processing Model
Input (senses) → Decision-making (selective attention, memory) → Output (motor response) → Feedback → loops back to input. Types of Guidance
Visual (demonstration) | Verbal (instruction) | Manual (physical support) | Mechanical (use of equipment). Types of Feedback
Intrinsic (felt by performer) vs extrinsic (from coach). Knowledge of performance (technique) vs knowledge of results (outcome). Positive vs negative. Diet, Health & Drugs in Sport
Topics commonly tested in extended-response questions.
Balanced Diet for Performers
Carbohydrates (main energy source — 55–60%), proteins (growth & repair — 12–15%), fats (energy reserve — 25–30%), plus vitamins, minerals, fibre and water. Hydration
Dehydration impairs performance — drink before, during and after activity. Sports drinks supply fluid, electrolytes and carbohydrate for events > 60 minutes. Performance-Enhancing Drugs (PEDs)
Anabolic steroids
Build muscle — risks: liver damage, aggression, infertility Stimulants
Reduce fatigue, increase alertness — risks: addiction, heart problems Beta blockers
Reduce HR, steady aim — used in archery/shooting Diuretics
Lose weight quickly, mask other drugs — risk: dehydration EPO / blood doping
Increases red-blood-cell count and O₂ delivery — risk: blood clots How to Use This Formula Sheet
Boost your Cambridge exam confidence with these proven study strategies from our tutoring experts.
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Label Diagrams Until Effortless
Practise labelling the skeleton, major muscle groups and the heart until you can do it from memory. Diagram-labelling questions are quick marks if recall is automatic.
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Drill the Formulas Daily
Max HR, target zones, cardiac output and BMI come up most years. Spend 5 minutes a day on calculation practice for guaranteed marks.
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Pair Each Fitness Component with a Test
For every component (agility, power, flexibility…) memorise the named test. Examiners frequently ask you to identify or evaluate the correct test.
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Use Your Practical Sport for Examples
When asked to apply theory, draw on your assessed sport. Concrete sporting examples earn AO2/AO3 marks more reliably than generic answers.
Formula Sheet FAQ
Quick answers about this free PDF and how to use it for exam revision and active recall.
Is the Cambridge IGCSE Physical Education Formula Sheet 2026 free to download as a PDF?
Yes. This Tutopiya formula sheet is free to use and you can download it as a PDF from this page for offline revision. There is no payment or account required for the PDF download.
What Physical Education topics and equations does this formula sheet cover?
This page groups key Physical Education formulas in one place for revision. Master Cambridge IGCSE Physical Education (0413) with this 2026 formula sheet. Covers anatomy & physiology, movement analysis, energy systems, fitness components, training principles and key calculations. Always cross-check with your official syllabus and past papers for your exam session.
Can I use this instead of the official exam formula booklet in the exam?
No. In the exam you must follow only what your exam board allows in the hall—usually the official formula booklet or data sheet where provided. This page is a revision and teaching aid, not a replacement for board-issued materials.
Who is this formula sheet for (Secondary)?
It is written for students preparing for assessments at Secondary in Physical Education, including classroom revision, homework support, and independent study. Teachers and tutors can also share it as a quick reference.
How should I revise with this formula sheet?
Work through past paper questions, quote the correct formula before substituting values, and check units and notation every time. Pair this sheet with timed practice and mark schemes so you see how examiners expect working to be set out.
Where can I get more help with Physical Education revision?
Explore Tutopiya’s study tools, past paper finder, and revision checklists linked from our tools hub, or book a trial lesson with a subject specialist for personalised support alongside this formula reference.
Need Help with Cambridge IGCSE Physical Education?
Work through anatomy, training theory and exam technique with an experienced Cambridge IGCSE PE tutor. We focus on diagram labelling, calculations and applying theory to your assessed sport.
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This formula sheet aligns with Cambridge Assessment International Education IGCSE Physical Education (0413) syllabus content for the 2026 exam series.
Always show working in numerical questions and apply theory to your chosen practical sport in extended-response answers.