📚 IGCSE OCR Geography: Formulae & Theorems Quick Reference | IGCSE OCR 地理：公式定理速查手册
This quick reference guide compiles the essential formulae and theorems required for IGCSE OCR Geography. It covers population, urbanisation, map skills, fieldwork and climate calculations. A firm grasp of these will support both your written examinations and fieldwork analysis.
本速查手册汇集了 IGCSE OCR 地理课程中的核心公式和定理，涵盖人口、城市化、地图技能、野外考察和气候计算。牢固掌握这些内容将为你的笔试和实地分析提供有力支持。
1. Population Density | 人口密度
Population density indicates how crowded an area is. It is found by dividing the total number of people by the land area they occupy.
人口密度显示了一个地区的拥挤程度，用总人口除以所占土地面积得到。
Population Density = Total Population / Land Area (people per km²)
土地面积通常以平方公里为单位，人口密度单位为人/平方公里。注意，可用总面积或仅可居住面积，考试中需根据问题说明选用。
人口密度 = 总人口 / 土地面积 (人/km²)
2. Crude Birth Rate (CBR) and Crude Death Rate (CDR) | 粗出生率与粗死亡率
The crude birth rate is the number of live births per 1000 people per year. The crude death rate is the number of deaths per 1000 people per year.
粗出生率指每年每千人中的活产婴儿数，粗死亡率指每年每千人中的死亡人数。
CBR = (Number of live births / Total population) × 1000
CDR = (Number of deaths / Total population) × 1000
两者均用千分率（‰）表示，方便跨国、跨地区比较。
粗出生率 = (活产婴儿数 / 总人口) × 1000
粗死亡率 = (死亡人数 / 总人口) × 1000
3. Natural Increase and Natural Increase Rate | 自然增长与自然增长率
Natural increase is the difference between the number of births and deaths in a population over a given period. The natural increase rate expresses this change per 1000 inhabitants.
自然增长是指一定时期内人口出生数与死亡数之差。自然增长率则将此变化表示为每千人的比值。
Natural Increase = Births − Deaths
Natural Increase Rate = CBR − CDR (per 1000)
当出生率大于死亡率时自然增长率为正；反之则人口自然减少。
自然增长 = 出生人数 − 死亡人数
自然增长率 = 粗出生率 − 粗死亡率 (每千人)
4. Net Migration Rate and Population Growth Rate | 净迁移率与人口增长率
Population change is also driven by migration. Net migration is the number of immigrants minus emigrants. Combining natural increase and net migration gives the overall population growth rate.
人口变动亦受迁移影响。净迁移量等于入境移民减去出境移民。将自然增长与净迁移相加，可得总人口增长率。
Net Migration = Immigrants − Emigrants
Net Migration Rate = (Net Migration / Total population) × 1000
Population Growth Rate = [(Natural Increase + Net Migration) / Total population] × 100 (%)
百分比增长率常用于评估人口翻倍时间。
净迁移量 = 入境移民 − 出境移民
净迁移率 = (净迁移量 / 总人口) × 1000
人口增长率 = [(自然增长 + 净迁移) / 总人口] × 100 (%)
5. Doubling Time (Rule of 70) | 人口倍增时间（70 法则）
The doubling time estimates how many years it will take for a population to double at a constant annual growth rate. The rule of 70 provides a simple approximation.
人口倍增时间用于估算在固定年增长率下人口翻一番所需的年数。70 法则给出了一种简便近似法。
Doubling Time (years) ≈ 70 / Annual growth rate (%)
例如，年增长率 2% 时，倍增时间约 35 年。该法则仅适用于指数增长情形。
倍增时间（年）≈ 70 / 年增长率 (%)
6. Dependency Ratio | 人口抚养比
The dependency ratio compares the economically dependent population (young and old) to the working-age population. It helps assess the pressure on the productive sector.
人口抚养比将经济上受供养的人口（少儿与老人）与劳动适龄人口进行比较，用以衡量生产性部门承受的压力。
Dependency Ratio = [(Population 0–14 + Population 65+) / Population 15–64] × 100
比值越高，每百名劳动人口需抚养的非劳动人口越多。
抚养比 = [(0–14 岁人口 + 65 岁以上人口) / 15–64 岁人口] × 100
7. Level of Urbanisation | 城市化水平
The level of urbanisation shows what proportion of a country’s population lives in urban areas. It is a key indicator of development.
城市化水平反映一个国家城市人口占总人口的比例，是衡量发展程度的关键指标。
Level of Urbanisation = (Urban population / Total population) × 100%
注意该指标是静态百分比；城市化速率（urbanisation rate）则是城市人口的年均增长率，需分开理解。
城市化水平 = (城市人口 / 总人口) × 100%
8. Map Scale and Distance | 地图比例尺与实地距离
A map scale expresses the ratio between a distance on the map and the corresponding distance on the ground. You can use it to convert measurements into real-world distances.
地图比例尺表示图上距离与对应实地距离的比值，可用于将图上量测的长度转换为实际距离。
Real distance (km) = (Map distance in cm × Scale denominator) / 100,000
例如，在 1:50,000 地图上，1 cm 代表实地 0.5 km。考试中务必注意单位换算。
实地距离 (km) = (图上距离 cm × 比例尺分母) / 100,000
9. Gradient (Slope) | 坡度/梯度
Gradient describes the steepness of a slope. It is the ratio of vertical rise to horizontal distance. In geography fieldwork, it is commonly used for hillslopes, river valleys and beach profiles.
梯度（坡度）描述斜坡的陡峭程度，即垂直上升高度与水平距离的比值。在地理实地考察中，常用于山坡、河谷和海滩剖面。
Gradient = Vertical difference (rise) / Horizontal distance (run)
结果常表示为 1:x 的比式，如 1:10 意指水平每 10 m，垂直上升 1 m。
梯度 = 垂直高差 / 水平距离
10. River Discharge | 河流流量
River discharge is the volume of water flowing through a channel cross-section per unit time. It is fundamental to hydrology and flood studies.
河流流量是单位时间内通过某一河道横截面的水体体积，是水文学和洪水研究的基础。
Discharge (Q) = Cross‑sectional Area (A) × Mean Velocity (V)
单位通常为立方米每秒（m³/s）。面积通过河道测量获得，流速可用浮标或流速仪测定。
流量 (Q) = 横截面积 (A) × 平均流速 (V)
11. Cross-sectional Area of a River | 河道横截面积
To calculate discharge, you first need the cross‑sectional area. The simplest approximation multiplies width by mean depth. A more accurate method divides the channel into vertical sections.
要计算流量，需先求得横截面积。最简单的近似方法是用宽度乘以平均深度；更精确的方法是将河道分成若干垂直条带分别计算。
Area ≈ Width × Average Depth
Area = Σ (segment width × mean depth of segment)
在野外考察中，每隔一定距离测量深度，再求和即可得到较为准确的面积。
面积 ≈ 宽度 × 平均深度
面积 = Σ (分段宽度 × 该段平均深度)
12. Temperature Range | 气温较差
Temperature range measures the variation in air temperature over a day (diurnal range) or a year (annual range). It is a simple but important climatic descriptor.
气温较差衡量一天（日较差）或一年（年较差）内的气温变化幅度，是简单而重要的气候特征指标。
Diurnal Temperature Range = Max. temperature − Min. temperature (in 24 hours)
Annual Temperature Range = Mean max. of warmest month − Mean min. of coldest month
单位均为摄氏度（°C）。内陆地区年较差通常大于沿海地区。
日较差 = 当日最高气温 − 当日最低气温
年较差 = 最热月平均最高温 − 最冷月平均最低温
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