📚 KS3 CIE Physical Education: Quick Reference Formula Handbook | KS3 CIE 体育：公式定理速查手册
Welcome to the ultimate quick reference guide for KS3 CIE Physical Education. This handbook brings together all the essential formulas, principles, and calculation methods you will encounter in your PE theory lessons and practical assessments. From heart rate zones and body composition to energy systems and training principles, every key concept is presented with clear explanations and worked examples. Understanding these formulas is not just about memorising numbers. It is about gaining a deeper insight into how the human body responds to exercise, how to measure performance accurately, and how to design effective training programmes. Use this guide regularly alongside your class notes and revision materials to build confidence for both written examinations and practical evaluations.
欢迎使用 KS3 CIE 体育终极速查指南。本手册汇集了你在体育理论课和实践评估中会遇到的所有基本公式、原理和计算方法。从心率区间和身体成分到能量系统和训练原则，每一个关键概念都配有清晰的解释和计算示例。理解这些公式不仅仅是记住数字那么简单。它关乎更深入地洞察人体如何对运动作出反应、如何准确测量运动表现以及如何设计有效的训练计划。请将本指南与你的课堂笔记和复习材料结合使用，为笔试和实践评估建立信心。
1. Maximum Heart Rate (MHR) | 最大心率 (MHR)
The maximum heart rate is the highest number of beats per minute your heart can achieve during all-out exercise. It provides the baseline for setting training intensity zones. The most commonly used estimation formula is: MHR = 220 − age. For a 12-year-old student, this gives MHR = 220 − 12 = 208 beats per minute. This is a population-average estimate, and individual variation exists. Nonetheless, it remains the standard starting point for KS3 PE heart rate calculations. Accurate MHR estimation helps you avoid overtraining and ensures you work at the right intensity for your fitness goals.
最大心率是你的心脏在全力运动中每分钟所能达到的最高跳动次数。它为设定训练强度区间提供了基准。最常用的估算公式是：MHR = 220 − 年龄。对于一名12岁的学生，计算得出 MHR = 220 − 12 = 208 次/分钟。这是一个人群平均值的估算，个体差异是存在的。尽管如此，它仍然是 KS3 体育心率计算的标准起点。准确估算 MHR 有助于你避免过度训练，并确保你以适合自己健身目标的强度进行锻炼。
MHR = 220 − Age (in years)
2. Target Heart Rate Zone (Karvonen Formula) | 靶心率区间（卡沃宁公式）
The Karvonen formula uses heart rate reserve to calculate target heart rate zones more precisely than simple percentages of MHR. First, find your resting heart rate by measuring your pulse first thing in the morning. Heart rate reserve is MHR minus resting heart rate. Target heart rate equals resting heart rate plus the desired percentage of heart rate reserve. For a 12-year-old with a resting heart rate of 70 bpm, MHR is 208 bpm, so heart rate reserve is 138 bpm. To train at 60% intensity, target heart rate = 70 + (0.6 × 138) = 152.8 bpm, rounded to 153 bpm. Lower-intensity aerobic work typically uses 50–70%, while higher-intensity intervals might target 70–85% of heart rate reserve.
卡沃宁公式利用心率储备来更精确地计算靶心率区间，比简单使用 MHR 百分比更为准确。首先，通过早晨起床后立即测量脉搏来获得静息心率。心率储备等于 MHR 减去静息心率。靶心率等于静息心率加上所需的心率储备百分比。对于一名静息心率为 70 bpm 的12岁学生，MHR 为 208 bpm，因此心率储备为 138 bpm。若以60%强度训练，靶心率 = 70 + (0.6 × 138) = 152.8 bpm，四舍五入为 153 bpm。低强度有氧训练通常使用 50–70%，而高强度间歇训练可能瞄准心率储备的 70–85%。
THR = RHR + (Intensity% × (MHR − RHR))
3. Body Mass Index (BMI) | 身体质量指数 (BMI)
Body Mass Index is a simple screening tool used to categorise individuals as underweight, healthy weight, overweight, or obese based on height and mass. The BMI formula is mass in kilograms divided by height in metres squared. For a student weighing 45 kg with a height of 1.55 m, BMI = 45 ÷ (1.55²) = 45 ÷ 2.4025 = 18.7 kg/m². This falls within the healthy weight range for children and adolescents, though exact interpretations depend on age- and sex-specific centile charts. KS3 students should understand that BMI does not distinguish between muscle and fat mass. A highly muscular young athlete could have a high BMI without excess body fat. Therefore, BMI is a population-level tool, not a diagnostic instrument for individuals.
身体质量指数是一种简单的筛查工具，用于根据身高和体重将个体划分为偏瘦、健康体重、超重或肥胖。BMI 公式为：体重公斤数除以身高米数的平方。对于一名体重45公斤、身高1.55米的学生，BMI = 45 ÷ (1.55²) = 45 ÷ 2.4025 = 18.7 kg/m²。该值落在儿童和青少年健康体重范围内，但具体解读须参考年龄和性别专项百分位图表。KS3 学生应当理解 BMI 不能区分肌肉量和脂肪量。一位肌肉发达的青年运动员可能具有较高的 BMI 却没有多余体脂。因此，BMI 是一种群体层面的工具，而非针对个体的诊断手段。
BMI = Mass (kg) ÷ Height² (m²)
4. Pace and Speed Calculation | 配速与速度计算
Pace and speed are fundamental concepts in athletics and cross-country. Speed measures how fast you cover a distance, while pace expresses how long it takes to cover a standard unit of distance. Speed = distance ÷ time. Pace = time ÷ distance. If a runner completes 1500 metres in 6 minutes (360 seconds), speed = 1500 ÷ 360 = 4.17 metres per second. Pace = 360 seconds ÷ 1500 metres = 0.24 seconds per metre, typically converted to minutes per kilometre by multiplying by 1000 and dividing by 60, giving 4 minutes per kilometre. KS3 students should practise converting between different units. Remember that 1 minute = 60 seconds, 1 kilometre = 1000 metres, and 1 hour = 3600 seconds. Clean unit conversions prevent careless errors in examinations.
配速和速度是田径运动和越野跑中的基本概念。速度衡量你覆盖一段距离的快慢，而配速表达的是覆盖一个标准距离单位所需的时间。速度 = 距离 ÷ 时间。配速 = 时间 ÷ 距离。如果一名跑者在6分钟（360秒）内完成1500米，速度 = 1500 ÷ 360 = 4.17 米/秒。配速 = 360秒 ÷ 1500米 = 0.24 秒/米，通常乘以1000再除以60转换为每公里分钟数，结果为每公里4分钟。KS3 学生应练习在不同单位之间进行转换。记住 1分钟 = 60秒，1公里 = 1000米，1小时 = 3600秒。清晰整洁的单位换算可以防止考试中的粗心错误。
Speed = Distance ÷ Time
Pace = Time ÷ Distance
5. Power-to-Weight Ratio | 功率体重比
Power-to-weight ratio measures how much power an athlete can produce relative to their body mass. It is particularly important in cycling, rowing, and climbing events where overcoming gravity is a major factor. The formula divides power output in watts by body mass in kilograms. A young cyclist producing 180 watts while weighing 50 kg has a power-to-weight ratio of 3.6 watts per kilogram. Higher ratios generally indicate better performance in uphill sections. Training to improve this ratio involves either increasing sustainable power output through strength and interval work, or reducing non-functional body mass through appropriate nutrition, or ideally both. KS3 students should note that rapid weight loss in growing adolescents is not recommended. Focus on developing power through safe, age-appropriate training.
功率体重比衡量的是运动员相对于其体重所能产生的功率。它在自行车、划船和登山等需要克服重力的项目中尤为重要。公式为：输出功率（瓦特）除以体重（公斤）。一名年轻自行车运动员体重50公斤，输出180瓦特，其功率体重比为3.6瓦/公斤。更高的比值通常预示着更好的上坡赛段表现。提高这一比值的训练包括通过力量训练和间歇训练来增加可持续输出功率，或者通过适当的营养管理减少非功能性体重，最理想的是两者兼而有之。KS3 学生应当注意，不建议处于生长发育期的青少年快速减重。应将重点放在通过安全且适合年龄的训练来发展功率输出。
PWR = Power Output (W) ÷ Body Mass (kg)
6. Calorie Expenditure and METs | 卡路里消耗与代谢当量
Physical activities burn energy, and understanding energy expenditure helps in planning balanced nutrition alongside exercise. One MET (Metabolic Equivalent of Task) represents the energy cost of sitting quietly, approximately 1 kilocalorie per kilogram of body mass per hour. Activities are rated by their MET values. Jogging might have a MET value of 7, meaning it burns about 7 kcal per kg per hour. To estimate calorie expenditure, multiply MET value by body mass in kilograms and by duration in hours. A student weighing 45 kg jogging at 7 METs for 30 minutes (0.5 hours) expends approximately 7 × 45 × 0.5 = 157.5 kilocalories. KS3 examinations may ask you to compare the energy cost of different activities using given MET tables. Always check that time units match. Convert minutes to hours by dividing by 60.
身体活动会消耗能量，了解能量消耗有助于在运动的同时规划均衡的营养摄入。一个 MET（任务代谢当量）代表安静坐着时的能量消耗，约等于每公斤体重每小时消耗1千卡。运动项目通过其 MET 值来进行评级。慢跑可能具有7 MET 值，意味着它大约每小时每公斤燃烧7千卡。要估算卡路里消耗，将 MET 值乘以体重公斤数和时长小时数。一名体重45公斤的学生以7 METs 慢跑30分钟（0.5小时），消耗约 7 × 45 × 0.5 = 157.5 千卡。KS3 考试可能会要求你使用给定的 MET 表格来比较不同运动的能量消耗。务必检查时间单位是否匹配。分钟除以60即可转换为小时。
Energy (kcal) = METs × Mass (kg) × Time (hours)
7. Hardy-Weinberg Principle in Talent Identification | 哈迪-温伯格原则在人才识别中的应用
Though originally from population genetics, the Hardy-Weinberg principle can inform discussions about genetic predispositions in sport. The equation p² + 2pq + q² = 1 describes the expected distribution of genotypes in a stable population, where p represents the frequency of one allele and q the frequency of the alternative allele, with p + q = 1. In PE contexts, students might discuss how certain genetic traits can influence sporting success, while understanding that environment, training, and opportunity play enormous roles. This equation provides a mathematical model for predicting how common a particular genotype might be in a population. KS3 students are not expected to perform complex Hardy-Weinberg calculations, but understanding the principle helps in discussing nature versus nurture debates in sport. Remember that the model assumes no mutation, no migration, random mating, large population size, and no natural selection, conditions rarely met in real human populations.
尽管哈迪-温伯格原则最初源于群体遗传学，但它可以为体育运动中关于遗传倾向的讨论提供参考。方程 p² + 2pq + q² = 1 描述了一个稳定群体中基因型的预期分布，其中p代表一种等位基因的频率，q代表另一种等位基因的频率，且 p + q = 1。在体育课程情境中，学生可以讨论某些遗传特质如何可能影响运动成就，同时理解环境、训练和机遇也发挥着巨大作用。这个公式为预测某一特定基因型在群体中的出现频率提供了一个数学模型。KS3 学生不需要进行复杂的哈迪-温伯格计算，但理解该原则有助于参与关于体育中先天与后天因素的讨论。请记住，该模型假设没有突变、没有迁移、随机婚配、大群体规模以及没有自然选择，而这些条件在真实人类群体中很少同时满足。
p² + 2pq + q² = 1
p + q = 1
8. FITT Principle for Training Programme Design | 训练计划设计的 FITT 原则
The FITT principle provides a structured framework for designing exercise programmes. FITT stands for Frequency, Intensity, Time, and Type. Frequency is how often you train per week. Intensity refers to how hard you work during each session, often expressed as a percentage of maximum heart rate, rate of perceived exertion on a Borg scale of 6 to 20, or a simpler 1-to-10 scale. Time is the duration of each training session. Type describes the mode of exercise, such as running, swimming, cycling, or resistance training. To improve cardiovascular fitness, a KS3 student might apply FITT as Frequency of 3 to 5 times per week, Intensity at 60–80% of MHR, Time of 20 to 40 minutes per session, and Type as continuous running or cycling. Progressive overload is achieved by gradually increasing one or more of these variables. KS3 exam questions often ask you to apply the FITT principle to a specific sport or fitness goal.
FITT 原则为设计训练计划提供了一个结构化的框架。FITT 代表频率、强度、时间和类型。频率指你每周训练的次数。强度指你每次训练的努力程度，通常以最大心率百分比、感知劳累评级法中的博格量表6至20分或更简单的1至10分制来表示。时间指每次训练的持续时间。类型描述的是运动模式，如跑步、游泳、骑行或阻力训练。为提升心血管适能，一名 KS3 学生应用 FITT 可以是频率为每周3至5次，强度为 MHR 的60–80%，时间为每次20至40分钟，类型为持续跑步或骑行。渐进性超负荷可以通过逐步增加上述一个或多个变量来实现。KS3 考试题目常要求你将 FITT 原则应用于某一特定运动或健身目标。
F = Frequency (sessions per week)
I = Intensity (% MHR or RPE)
T = Time (minutes per session)
T = Type (mode of exercise)
Body composition describes the proportion of fat mass to fat-free mass in the body. Fat-free mass includes muscles, bones, organs, and water. Lean body mass is essentially body mass minus fat mass. The formula is straightforward: Lean Body Mass = Total Body Mass − Fat Mass. Fat mass can be estimated through skinfold caliper measurements, bioelectrical impedance scales, or hydrostatic weighing. For example, a student weighing 50 kg with 20% body fat has a fat mass of 10 kg and a lean body mass of 40 kg. Understanding body composition is more informative than BMI alone for athletes, as two individuals with identical BMI can have vastly different proportions of muscle and fat. KS3 students learn that healthy body composition ranges differ between males and females and change throughout adolescence. Maintaining a sport-appropriate body composition through balanced nutrition and training supports both health and performance.
身体成分描述的是体内脂肪质量与去脂质量的比例。去脂质量包括肌肉、骨骼、器官和水分。瘦体重实质上等于总体重减去脂肪质量。公式很简单：瘦体重 = 总体重 − 脂肪质量。脂肪质量可以通过皮褶卡尺测量、生物电阻抗秤或水下称重法来估算。举例来说，一名体重50公斤、体脂率为20%的学生，其脂肪质量为10公斤，瘦体重为40公斤。对运动员而言，了解身体成分比单纯看 BMI 更具信息价值，因为两个 BMI 相同的人可能拥有截然不同的肌肉与脂肪比例。KS3 学生将学到，健康的身体成分范围因性别而异，并在整个青春期不断变化。通过均衡营养和训练维持适合所从事运动的身体成分，能够同时促进健康和运动表现。
LBM = Total Mass − Fat Mass
Body Fat% = (Fat Mass ÷ Total Mass) × 100
Maintaining hydration is critical for both performance and safety in sport. Fluid loss during exercise can be estimated by measuring body mass before and after activity. Each kilogram of body mass lost corresponds to approximately 1 litre of fluid loss. The formula is: Fluid Loss (litres) = Pre-exercise Mass (kg) − Post-exercise Mass (kg). A footballer who weighs 52 kg before a match and 51.2 kg afterwards has lost 0.8 kg, equivalent to about 800 millilitres of fluid. To fully rehydrate, athletes are advised to consume 1.2 to 1.5 litres of fluid for every kilogram of body mass lost, accounting for ongoing urine production. KS3 students should note that thirst is not a reliable indicator of hydration status. Urine colour charts offer a practical field method for monitoring hydration. Pale straw-coloured urine generally indicates good hydration, while dark yellow or brown urine suggests significant dehydration requiring immediate fluid intake.
保持水分对运动表现和安全都至关重要。运动中流失的液体可以通过测量运动前后的体重来估算。每公斤体重下降大约对应1升的液体流失。公式为：流体流失量（升）= 运动前体重（公斤）− 运动后体重（公斤）。一名足球运动员赛前体重52公斤、赛后体重51.2公斤，流失了0.8公斤，相当于约800毫升液体。为了充分补充水分，建议运动员每公斤体重流失补充1.2至1.5升液体，以弥补持续产生的尿液。KS3 学生应注意，口渴并不是判断水合状态的可靠指标。尿液颜色表提供了一种实用的现场检测方法：淡稻草色尿液通常表示水分充足，而深黄或棕色尿液则表明存在显著脱水，需要立即摄入液体。
Fluid Loss (L) = Pre-Exercise Mass (kg) − Post-Exercise Mass (kg)
Maximal oxygen uptake, or VO₂max, is a key indicator of aerobic endurance. It represents the maximum volume of oxygen the body can utilise per minute per kilogram of body mass during intense exercise. Direct measurement requires laboratory equipment, but field-based estimations are accessible for KS3 students. The Cooper 12-minute run test provides one such estimation. The formula is: VO₂max (ml/kg/min) = (Distance covered in metres − 504.9) ÷ 44.73. If a student covers 2400 metres in 12 minutes, VO₂max = (2400 − 504.9) ÷ 44.73 = 1895.1 ÷ 44.73 = 42.4 ml/kg/min. Alternative field tests include the multi-stage fitness test, known as the bleep test, which uses the final shuttle level and number to estimate VO₂max through pre-calculated conversion tables. Higher VO₂max values generally correlate with better performance in endurance events such as distance running, cycling, and swimming. Training can improve VO₂max by 5–20% depending on initial fitness level, genetics, and training quality.
最大摄氧量 (VO₂max) 是有氧耐力的关键指标。它代表在高强度运动中身体每分钟每公斤体重所能使用的最大氧气量。直接测量需要实验室设备，但基于场地的估算方法对 KS3 学生来说是可行的。库珀12分钟跑测试就提供了这样一种估算方法。公式为：VO₂max（毫升/公斤/分钟）=（完成的距离（米）− 504.9）÷ 44.73。如果一名学生在12分钟内跑了2400米，VO₂max = (2400 − 504.9) ÷ 44.73 = 1895.1 ÷ 44.73 = 42.4 毫升/公斤/分钟。其他场地测试包括多阶段体能测试，即 bleep test，它使用最终的折返跑层级和次数，通过预设计算表格来估算 VO₂max。较高的 VO₂max 值通常与长跑、骑行、游泳等耐力项目的更好表现呈正相关。根据初始体能水平、基因和训练质量，训练可将 VO₂max 提升 5–20%。
VO₂max = (Distance in metres − 504.9) ÷ 44.73
Carbohydrate loading is a nutritional strategy used by endurance athletes to maximise muscle glycogen stores before a prolonged event lasting 90 minutes or more. The recommended intake is approximately 8 to 12 grams of carbohydrate per kilogram of body mass per day during the loading phase, which typically begins 36 to 48 hours before competition. For a 50 kg young triathlete, this means consuming 400 to 600 grams of carbohydrate daily. Energy availability is a broader concept defined as dietary energy intake minus exercise energy expenditure, divided by fat-free mass. The formula is: Energy Availability (kcal/kg FFM/day) = (Energy Intake − Exercise Energy Expenditure) ÷ Fat-Free Mass. Optimal energy availability for health and performance is generally above 45 kcal/kg FFM/day for adolescents, though exact recommendations vary. Values below 30 kcal/kg FFM/day are associated with Relative Energy Deficiency in Sport, a condition affecting hormonal function, bone health, and performance. KS3 students should approach these concepts with an understanding that growing bodies have high energy and nutrient demands, and extreme dietary manipulation is not appropriate without professional supervision.
碳水化合物负荷是一种营养策略，耐力运动员在持续90分钟或更长时间的赛事开始前，通过此策略来最大化肌肉糖原储备。建议摄入量约为每天每公斤体重8至12克碳水化合物，负荷阶段通常从赛前36至48小时开始。对于一名体重50公斤的少年铁人三项运动员，这意味着每天摄入400至600克碳水化合物。能量可用性是一个更广泛的概念，定义为膳食能量摄入减去运动能量消耗，再除以去脂体重。公式为：能量可用性（千卡/公斤去脂体重/天）=（能量摄入−运动能量消耗）÷ 去脂体重。对于青少年而言，维持健康和运动表现的最佳能量可用性通常在每天每公斤去脂体重45千卡以上，但具体建议存在差异。低于每天每公斤去脂体重30千卡的值与运动相对能量不足症候群相关，这种状况会影响激素功能、骨骼健康和运动表现。KS3 学生在接触这些概念时应当明白，成长中的身体对能量和营养素的需求很高，在缺乏专业指导的情况下进行极端饮食操控是不恰当的。
CHO Loading = 8–12 g per kg Body Mass per day
EA = (EI − EEE) ÷ FFM
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