📚 IGCSE Cambridge Geography: Formula & Theorem Quick Reference | IGCSE 剑桥地理：公式定理速查手册
This quick-reference guide collects the essential calculations, indicators and fieldwork statistics most commonly tested in Cambridge IGCSE Geography. It covers population, urban settlement, rivers, map skills and data analysis. For every formula, learn the meaning of each term, the correct units and a worked example so you can apply it confidently in Papers 1, 2 and 4.
本速查手册汇总了剑桥 IGCSE 地理中最常考的必会计算、指标和野外调查统计方法，涵盖人口、城市聚落、河流、地图技能和数据分析。对于每个公式，都要掌握各项目的含义、正确单位和计算示例，才能在 Paper 1、Paper 2 和 Paper 4 中熟练运用。
1. Population Density | 人口密度
Population density measures how crowded an area is. It is one of the most common calculations in IGCSE Geography and may use data for countries, regions or cities.
人口密度衡量一个地区的拥挤程度。这是 IGCSE 地理中最常见的计算之一，可能使用国家、地区或城市的数据。
Population density = Total population ÷ Land area
人口密度 = 总人口 ÷ 土地面积
The population is the total number of people, and land area is usually given in square kilometres (km²). The result is therefore expressed as people per km². Always check that both the total population and area refer to the same place and time.
人口是总人数，土地面积通常以平方千米（km²）表示。因此结果用每平方千米人数表示。务必检查总人口和面积是否指同一地点和同一时间。
2,000,000 ÷ 50,000 = 40 people per km². This can be described as a relatively low density.
例如，某地区有 2,000,000 人，面积为 50,000 km²，则人口密度 = 2,000,000 ÷ 50,000 = 40 人/km²。这属于相对较低的人口密度。
2. Crude Birth Rate, Crude Death Rate and Natural Increase | 出生率、死亡率和自然增长率
These vital rates are usually expressed per 1000 people per year. Using a common base of 1000 allows fair comparison between countries of different population sizes.
这些生命统计率通常以每年每千人为单位表示。使用每千人这一共同基数，可以在人口规模不同的国家之间进行公平比较。
birth rate (CBR) = (Number of live births in one year ÷ Total mid-year population) × 1000
粗出生率（CBR）=（一年内活产婴儿数 ÷ 年中总人口）× 1000
Crude death rate (CDR) = (Number of deaths in one year ÷ Total mid-year population) × 1000
粗死亡率（CDR）=（一年内死亡人数 ÷ 年中总人口）× 1000
Natural increase per 1000 = CBR − CDR
每千人自然增长 = 出生率 − 死亡率
Natural increase rate (%) = [(Births − Deaths) ÷ Total mid-year population] × 100
自然增长率（%）= [（出生人数 − 死亡人数）÷ 年中总人口] × 100
R = (4,000 ÷ 500,000) × 1000 = 8 per 1000. Natural increase = 20 − 8 = 12 per 1000, or 1.2% per year.
某镇年中人口为 500,000，一年内有 10,000 名活产婴儿和 4,000 人死亡。CBR =（10,000 ÷ 500,000）× 1000 = 20‰。CDR =（4,000 ÷ 500,000）× 1000 = 8‰。自然增长 = 20 − 8 = 12‰，即每年 1.2%。
- If birth rate exceeds death rate, natural increase is positive.
- 如果出生率高于死亡率，自然增长为正。
- If death rate exceeds birth rate, natural change is negative, sometimes called natural decrease.
- 如果死亡率高于出生率，自然变动为负，有时称为自然减少。
3. Population Growth Rate | 人口增长率
Population growth includes natural change plus net migration. It measures the percentage change in total population over a period, usually one year.
人口增长包括自然变动和净迁移。它衡量一定时期内总人口的百分比变化，通常以一年为单位。
Net migration = Immigration − Emigration
净迁移 = 迁入人口 − 迁出人口
Population growth rate (%) = [(Births − Deaths + Net migration) ÷ Population at start of period] × 100
人口增长率（%）= [（出生人数 − 死亡人数 + 净迁移）÷ 期初人口] × 100
00 = 20,000. Population growth rate = (150,000 − 90,000 + 20,000) ÷ 10,000,000 × 100 = 0.8%.
如果某国年初人口为 10,000,000，全年出生 150,000 人，死亡 90,000 人，迁入 40,000 人，迁出 20,000 人，则净迁移 = 40,000 − 20,000 = 20,000。人口增长率 =（150,000 − 90,000 + 20,000）÷ 10,000,000 × 100 = 0.8%。
| Component | Formula | Interpretation |
| Natural change | Births − Deaths | Difference between births and deaths |
| Net migration | Immigration − Emigration | Difference between people entering and leaving |
| Population change | Births − Deaths + Net migration | Total increase or decrease |
4. Dependency Ratio | 抚养比
The dependency ratio compares the economically dependent age groups to the working-age population. It is usually expressed as the number of dependents per 100 people of working age.
抚养比将经济上受抚养的年龄组与劳动年龄人口进行比较，通常表示为每 100 名劳动年龄人口对应的受抚养人口数。
tio = [(Population aged 0−14 + Population aged 65 and over) ÷ Population aged 15−64] × 100
抚养比 = [（0−14 岁人口 + 65 岁及以上人口）÷ 15−64 岁人口] × 100
Young dependency ratio = (Population aged 0−14 ÷ Population aged 15−64) × 100
少儿抚养比 =（0−14 岁人口 ÷ 15−64 岁人口）× 100
Old dependency ratio = (Population aged 65 and over ÷ Population aged 15−64) × 100
老年抚养比 =（65 岁及以上人口 ÷ 15−64 岁人口）× 100
0 × 100 = 66.7. This means there are about 67 dependents for every 100 working-age people.
如果某国人口为 1,000,000：其中 0−14 岁 250,000 人，15−64 岁 600,000 人，65 岁及以上 150,000 人，则抚养比 =（250,000 + 150,000）÷ 600,000 × 100 = 66.7。这意味着每 100 名劳动年龄人口对应约 67 名受抚养人口。
A high dependency ratio may indicate greater pressure on health, education and pension services, especially if many dependents are young or elderly.
高抚养比可能表明医疗、教育和养老服务的压力更大，尤其是当受抚养人口中儿童或老年人较多时。
5. Infant Mortality Rate and Total Fertility Rate | 婴儿死亡率和总和生育率
Infant mortality rate (IMR) is a powerful development indicator. It measures the number of deaths of infants under one year of age per 1000 live births in the same year.
婴儿死亡率（IMR）是一个非常有用的发展指标。它表示同一年中每 1000 名活产婴儿中未满一周岁死亡的人数。
(Number of deaths of infants under 1 year ÷ Number of live births in the same year) × 1000
婴儿死亡率 =（同一年未满 1 岁婴儿死亡人数 ÷ 同一年活产婴儿数）× 1000
1000 live births. A low IMR usually suggests better healthcare, nutrition and sanitation.
某地区一年内有 200 名婴儿死亡和 25,000 名活产婴儿，则 IMR =（200 ÷ 25,000）× 1000 = 8‰ 活产婴儿
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