📚 Year 12 Cambridge Geography: Essential Formulae & Theorems Quick Reference | Year 12 剑桥地理：公式定理速查手册
This quick reference handbook brings together the key formulae, equations and conceptual theorems required for the Year 12 Cambridge International AS Level Geography course (9696). Use it to reinforce your understanding of physical and human geography calculations – from river discharge and water balance to population rates and risk assessment. Every entry is presented with a clear explanation, common units and practical tips for exam success.
本速查手册汇集了 Year 12 剑桥国际 AS 地理课程 (9696) 所需的核心公式、方程与概念定理。用它来巩固自然地理和人文地理计算——从河流流量、水量平衡到人口统计与风险评估。每个条目都配有清晰的说明、常用单位以及助你考试的实用要点。
1. Discharge (Flow) Formula | 流量公式
The discharge (Q) of a river – the volume of water passing a point per unit time – forms the basis for most fluvial studies. It is calculated as:
河流流量(Q)——单位时间内通过某一点的水体体积——是大多数河流研究的基础。其计算公式为：
Q = A × V
where A is the cross‑sectional area of the channel (m²) and V is the mean velocity (m/s). Discharge is normally expressed in cubic metres per second (m³/s).
其中 A 为河道横截面积(m²)，V 为平均流速(m/s)。流量通常以立方米每秒(m³/s)表示。
To determine A in the field, measure the width (w) of the channel and the average depth (d) at regular intervals, then apply:
在野外确定 A 时，需测量河道宽度(w)并按固定间隔测定平均水深(d)，然后计算：
A = w × d
Velocity can be obtained using a flowmeter or by timing a float over a known distance and multiplying by a correction factor (typically 0.85 for rough beds).
流速可用流速计测量，或通过计时浮标漂过已知距离并乘以修正系数（粗糙河床通常为 0.85）获得。
2. Catchment Water Balance | 流域水量平衡
The water balance equation expresses the principle of conservation of mass within a drainage basin over a given time period:
水量平衡方程表达了特定时段内流域质量守恒的原理：
P = Q + E + ΔS
where P is precipitation, Q is runoff, E is evapotranspiration, and ΔS is the change in storage (soil moisture, groundwater, surface reservoirs). All components are usually given in millimetres (mm) of water depth.
其中 P 为降水量，Q 为径流量，E 为蒸散发量，ΔS 为储水量变化（土壤水、地下水、地表水库）。所有分量通常以毫米(mm)水深表示。
A positive ΔS indicates a net gain in basin storage, while a negative value means the catchment is losing stored water. This theorem helps hydrologists predict river regimes and understand flood generation.
ΔS 为正表示流域储水净增加，为负则表示流域在释放蓄水。这一定理有助于水文工作者预测河流情势并理解洪水形成。
3. Runoff Coefficient | 径流系数
The runoff coefficient measures the proportion of precipitation that becomes surface runoff. It is a dimensionless value reflecting catchment characteristics such as impermeability, slope and soil moisture:
径流系数衡量降水中转化为地表径流的比例。这是一个无量纲值，反映流域特征如不透水性、坡度和土壤湿度：
C = Q / P
where C is the runoff coefficient, Q is total runoff depth (mm) and P is total precipitation (mm). C ranges from 0 to 1 (or expressed as a percentage). Urban areas with extensive impervious surfaces often have C values above 0.7.
其中 C 为径流系数，Q 为总径流深(mm)，P 为总降水量(mm)。C 的取值范围为 0 至 1（也可表示为百分比）。拥有大面积不透水地表的城市区域 C 值常高于 0.7。
A low coefficient (e.g. 0.1–0.2) is typical of forested, well‑drained catchments, indicating high infiltration and low surface runoff.
低系数（例如 0.1–0.2）常见于植被覆盖良好、排水通畅的流域，表明入渗量高、地表径流少。
4. Gradient Calculation | 坡度计算
Slope gradient is a fundamental measure in both fluvial and slope geomorphology. It can be expressed as a ratio, a percentage or in degrees:
坡度是河流地貌和坡面地貌中的基本量度。可用比降、百分比或度数表示：
Gradient = Vertical rise ÷ Horizontal distance
For a percentage, multiply by 100. For a ratio, reduce the fraction so that the vertical rise is 1, e.g. a rise of 5 m over 100 m gives a gradient of 1 : 20.
若以百分比表示，则乘以 100。若以比降表示，则化简为使垂直上升量为 1 的分数，例如升高 5 m 而水平距离 100 m 时比降为 1 : 20。
In river studies, gradient influences velocity, competence and capacity. A steep gradient (e.g. 1 : 10) in upper courses promotes erosion, while a gentle gradient (e.g. 1 : 1000) in lower courses favours deposition.
在河流研究中，坡度影响流速、挟带力和输沙量。上游陡坡（如 1 : 10）促进侵蚀，而下游平缓坡度（如 1 : 1000）则利于沉积。
5. Crude Birth Rate & Death Rate | 出生率与死亡率
Crude birth rate (CBR) and crude death rate (CDR) are the simplest demographic measures, expressed per 1000 population per year:
粗出生率(CBR)和粗死亡率(CDR)是最简单的人口统计指标，以每年每千人表示：
CBR = (Number of live births ÷ Total population) × 1000
CDR = (Number of deaths ÷ Total population) × 1000
These rates are ‘crude’ because they do not account for the age structure of the population. A high CBR (above 30/1000) is typical of Stage 2 of the Demographic Transition Model, while a low CDR (below 10/1000) characterises many HICs.
这些比率之所以“粗”，是因为未考虑人口年龄结构。高CBR（高于 30‰）出现在人口转变模型的第二阶段，而低CDR（低于 10‰）则是许多高收入国家的特征。
Always ensure you present the final answer as a value per 1000, not as a decimal or percentage.
务必确保最终答案以千分比形式呈现，而非小数或百分比。
6. Natural Increase & Population Growth Rate | 自然增长率与人口增长率
Natural increase ignores migration and reflects the difference between births and deaths:
自然增长率忽略迁移，反映出生与死亡之差：
Natural increase = CBR − CDR
The rate of natural increase (RNI) is often expressed as a percentage:
自然增长率(RNI)常以百分比表示：
RNI (%) = (CBR − CDR) ÷ 10
To obtain the population growth rate, net migration must be added. In exam data‑response questions, you may need to calculate the overall annual growth rate as:
为求得人口增长率，需加上净迁移。在考试的数据回应题中，可能需要计算总体年增长率：
Growth rate (%) = {(CBR − CDR) + Net migration rate} ÷ 10
A positive growth rate indicates a growing population; a negative value suggests decline. This formula links with the population equation: P(t+1) = P(t) + (Births−Deaths) + (Immigration−Emigration).
正增长率表明人口增加，负值则意味着减少。该公式与人口方程相联系：P(t+1) = P(t) + (出生−死亡) + (迁入−迁出)。
7. Population Density | 人口密度
Population density describes the average number of people per unit area, providing a simple measure of pressure on land:
人口密度描述单位面积上平均居住的人数，是衡量土地压力的简单指标：
Population density = Total population ÷ Total land area (km²)
It is essential to use accurate mid‑year population estimates and to recognise that crude density masks local variation. High densities (e.g. >500 persons/km²) are typical of urban centres and fertile river valleys, while low densities are common in arid or mountainous regions.
必须使用准确的年中人口估算值，并认识到粗密度掩盖了局部差异。高密度（如 >500人/km²）常见于城市中心和肥沃河谷，而低密度则出现在干旱或山区。
Physiological density (population ÷ cultivable land area) offers a more refined picture of resource pressure, particularly in agricultural societies.
生理密度（人口 ÷ 可耕地面积）能更细致地反映资源压力，尤其在农业社会中。
8. Level of Urbanisation | 城市化水平
The level of urbanisation is the share of a country’s total population living in areas classified as urban:
城市化水平是指一国总人口中居住在被划为城市区域的人口比例：
Urbanisation level (%) = (Urban population ÷ Total population) × 100
Different countries adopt varying definitions of ‘urban’, so comparisons should be made with caution. In papers, you may also need to calculate the rate of urbanisation (% increase in urban population over time) as evidence of urban growth.
各国对“城市”的定义不尽相同，因此进行比较时需谨慎。在试卷中，你可能还需计算城市化速率（城市人口随时间增加的百分比）作为城市增长的证据。
High levels of urbanisation (above 75%) are characteristic of HICs, whereas rapid urbanisation rates are more common in MICs and LICs.
高城市化水平（高于 75%）是高收入国家的特征，而快速城市化速率则更常见于中等收入和低收入国家。
9. Dependency Ratio | 扶养比
The dependency ratio indicates the proportion of the population that is economically dependent on the working‑age group. It is widely used to assess the social and economic burden on the productive population:
扶养比反映依赖劳动适龄人口供养的人口比例，广泛用于评估社会经济负担：
Dependency ratio = {(Pop₀₋₁₄ + Pop₆₅₊) ÷ Pop₁₅₋₆₄} × 100
Here, Pop₀₋₁₄ is the population aged 0–14, Pop₆₅₊ is the population aged 65 and over, and Pop₁₅₋₆₄ is the working‑age population. The result is the number of dependants per 100 workers.
这里，Pop₀₋₁₄ 为 0–14 岁人口，Pop₆₅₊ 为 65 岁及以上人口，Pop₁₅₋₆₄ 为劳动适龄人口。计算结果为每百名劳动者的抚养人数。
Youth dependency is high in LEDCs; old‑age dependency is rising in many HICs. Both have significant implications for healthcare, education and pension systems.
欠发达国家青年抚养比高；而许多高收入国家的老年抚养比正在上升。两者对医疗、教育和养老金体系都有重大影响。
10. Migration Rate & Net Migration | 迁移率与净迁移
Migration statistics require careful handling of inflows and outflows. The crude net migration rate is calculated as:
迁移统计需谨慎处理流入与流出。粗净迁移率计算公式为：
Net migration rate = {(Immigrants − Emigrants) ÷ Total population} × 1000
A positive rate indicates net immigration; a negative rate shows net emigration. In addition, the net migration balance is simply I − E, where I is the number of immigrants and E is the number of emigrants.
正值为净迁入，负值为净迁出。此外，净迁移平衡即 I − E，其中 I 为迁入人数，E 为迁出人数。
Migration effectiveness can also be expressed as an effectiveness index: (I − E) ÷ (I + E) × 100. This helps compare the directional strength of population movement between regions.
迁移有效性也可用有效性指数表示：(I − E) ÷ (I + E) × 100。这有助于比较区域间人口迁移的方向强度。
11. Risk Assessment Formula | 风险评估公式
In the study of natural hazards, risk is often conceptualised as the product of hazard and vulnerability, moderated by capacity to cope:
在自然灾害研究中，风险常被定义为危险性与脆弱性的乘积，并受应对能力的调节：
Risk = Hazard × Vulnerability
Hazard represents the probability of a damaging event (e.g. earthquake magnitude‑frequency), while vulnerability refers to the susceptibility of people and assets. A more detailed expression sometimes includes adaptive capacity in the denominator:
Hazard 表示破坏性事件发生的概率（如地震震级‑频率），Vulnerability 指人口和资产的易损性。更详细的表述有时会将适应能力置于分母：
Risk = (Hazard × Vulnerability) ÷ Capacity
This theorem underpins disaster management strategies: reducing vulnerability or enhancing capacity lowers risk even if the hazard remains unchanged.
这一定理是灾害管理策略的基础：即使危险程度不变，降低脆弱性或增强能力也能降低风险。
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