📚 IGCSE CIE Geography: Formulae & Key Calculations Quick Reference | IGCSE CIE 地理：公式定理速查手册
This handbook compiles the essential formulae, key calculations and quick-reference methods required for the IGCSE CIE Geography syllabus. Whether you are analysing population change, measuring river characteristics, or interpreting statistical data, these equations will help you answer Paper 1, Paper 2 and Paper 4 questions accurately.
本手册汇集了IGCSE CIE地理大纲要求的核心公式、关键计算和速查方法。无论你是在分析人口变化、测量河流特征，还是解读统计数据，这些方程都能帮助你准确回答试卷一、试卷二和试卷四的题目。
1. Population Density | 人口密度
Population density measures how crowded an area is. It is calculated by dividing the total population by the total land area.
人口密度衡量一个地区的拥挤程度。它的计算方法是总人口除以土地总面积。
Population Density = Total Population ÷ Total Land Area (km²)
人口密度 = 总人口 ÷ 土地总面积 (km²)
Remember to check the units: area is usually given in km². If the area is in hectares or m², convert it to km² first (1 km² = 100 hectares = 1,000,000 m²).
注意检查单位：面积通常以平方公里为单位。如果给出的面积单位是公顷或平方米，需先转换为平方公里（1平方公里 = 100公顷 = 1,000,000平方米）。
2. Natural Increase Rate (%) | 自然增长率 (%)
The natural increase rate shows how fast a population is growing from births and deaths alone, excluding migration. It is expressed as a percentage.
自然增长率显示仅由出生和死亡导致的人口增长速度，不包括迁移。它以百分比表示。
Natural Increase Rate (%) = ((Number of Births − Number of Deaths) ÷ Total Population) × 100
自然增长率 (%) = ((出生人数 − 死亡人数) ÷ 总人口) × 100
This can also be calculated using Crude Birth Rate (CBR) and Crude Death Rate (CDR):
也可用粗出生率（CBR）和粗死亡率（CDR）计算：
Natural Increase Rate (%) = (CBR − CDR) ÷ 10
自然增长率 (%) = (粗出生率 − 粗死亡率) ÷ 10
Note: CBR and CDR are usually given per 1000 people. Dividing the difference by 10 converts it to a percentage.
注意：粗出生率和粗死亡率通常是以每千人为单位。将其差值除以10即转换为百分比。
3. Net Migration Rate | 净迁移率
Net migration rate expresses the difference between immigrants (people moving in) and emigrants (people moving out) per 1000 population.
净迁移率表示每千人中迁入人口与迁出人口的差值。
Net Migration Rate = ((Immigrants − Emigrants) ÷ Total Population) × 1000
净迁移率 = ((迁入人数 − 迁出人数) ÷ 总人口) × 1000
A positive value indicates net in-migration; a negative value indicates net out-migration. Sometimes the result is converted to a percentage by dividing by 10.
正值表示净迁入；负值表示净迁出。有时将结果除以10即可转换为百分比。
4. Population Growth Rate (%) | 人口增长率 (%)
Total population growth rate combines natural increase and net migration. It is the percentage change in total population over one year.
总人口增长率结合了自然增长和净迁移。它是总人口在一年内的百分比变化。
Population Growth Rate (%) = Natural Increase Rate (%) + (Net Migration Rate ÷ 10)
人口增长率 (%) = 自然增长率 (%) + (净迁移率 ÷ 10)
Or directly from absolute numbers:
或直接使用绝对数值计算：
Growth Rate (%) = ((Births − Deaths) + (Immigrants − Emigrants)) ÷ Total Population × 100
增长率 (%) = ((出生人数 − 死亡人数) + (迁入人数 − 迁出人数)) ÷ 总人口 × 100
5. Crude Birth Rate & Crude Death Rate (per 1000) | 粗出生率与粗死亡率 (每千人)
These rates allow comparisons between countries of different sizes. They are always expressed per 1000 people.
这些比率可用于比较不同规模的国家。它们总是以每千人为单位表达。
Crude Birth Rate (CBR) = (Number of Live Births ÷ Total Population) × 1000
粗出生率 (CBR) = (活产婴儿数 ÷ 总人口) × 1000
Crude Death Rate (CDR) = (Number of Deaths ÷ Total Population) × 1000
粗死亡率 (CDR) = (死亡人数 ÷ 总人口) × 1000
Be careful: if a question gives per 100 values, adjust accordingly. Standard CBR/CDR uses per 1000.
注意：如果题目给出的数值是每百人，需相应调整。标准粗出生率/粗死亡率使用每千人。
6. Infant Mortality Rate (IMR) | 婴儿死亡率
Infant mortality rate is the number of deaths of infants under one year of age per 1000 live births in a given year.
婴儿死亡率是指给定年份中每千名活产婴儿中一岁以下死亡的人数。
Infant Mortality Rate = (Deaths of infants < 1 year ÷ Number of Live Births) × 1000
婴儿死亡率 = (一岁以下婴儿死亡人数 ÷ 活产婴儿数) × 1000
This is an important indicator of healthcare quality and is often used alongside life expectancy in the Demographic Transition Model.
这是衡量医疗质量的重要指标，常与预期寿命一起用于人口转变模型。
7. Dependency Ratio | 抚养比
The dependency ratio compares the economically dependent population (young 0-14 and old 65+) to the working-age population (15-64). It is expressed as a ratio or percentage.
抚养比是指经济依赖型人口（0-14岁少儿和65岁以上老年）与劳动年龄人口（15-64岁）之比。它表示为比率或百分比。
Dependency Ratio (%) = ((Population aged 0−14 + Population aged 65+) ÷ Population aged 15−64) × 100
抚养比 (%) = ((0−14岁人口 + 65岁以上人口) ÷ 15−64岁人口) × 100
A high dependency ratio indicates greater pressure on the working population to support dependants. Sometimes the young and old dependency ratios are calculated separately.
抚养比高表明劳动人口抚养负担重。有时少儿抚养比和老年抚养比会分开计算。
8. River Discharge (Cumecs) | 河流流量（立方米/秒）
Discharge is the volume of water flowing through a river channel at a given point per unit of time. It is measured in cubic metres per second (cumecs).
流量是单位时间内流过河道某一断面的水量。它的单位是立方米每秒（cumecs）。
Discharge (Q) = Cross-sectional Area (A) × Mean Velocity (V)
流量 (Q) = 横截面积 (A) × 平均流速 (V)
Cross-sectional area (A) is calculated from width × average depth. Velocity (V) may be determined by float method or current meter. Units: A in m², V in m/s, giving Q in m³/s.
横截面积 (A) 由河宽 × 平均深度计算。流速 (V) 可通过浮标法或流速仪测定。单位：A（平方米），V（米/秒），得到流量 Q（立方米/秒）。
9. Gradient of a River | 河流坡度
Gradient describes the steepness of a river channel, usually expressed as a ratio, percentage or in degrees. It affects velocity and erosion.
坡度描述河道的陡峭程度，通常以比率、百分比或角度表示。它影响流速和侵蚀。
Gradient = Vertical Drop (height difference) ÷ Horizontal Distance
坡度 = 垂直落差 (高差) ÷ 水平距离
To express as a percentage: multiply by 100. For example, a drop of 50 m over 1 km (1000 m) gives a gradient of 0.05 or 5%.
以百分比表示：乘以100。例如，在1公里（1000米）的水平距离内落差50米，坡度为0.05或5%。
10. Percentage Change | 百分比变化
Percentage change is widely used in geography to describe population growth, urban expansion, economic change, etc.
百分比变化在地理中广泛用于描述人口增长、城市扩张、经济变化等。
Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100
百分比变化 = ((新值 − 原值) ÷ 原值) × 100
If the result is positive, it indicates an increase; if negative, a decrease. Always state the time period, e.g. ‘between 2000 and 2020, the population increased by 34%’.
结果为正值表示增加；负值表示减少。务必注明时间段，例如“2000年至2020年间，人口增长了34%”。
11. Speed, Distance, Time (for Transport & Migration) | 速度、距离、时间（用于交通与迁移）
Understanding movement of goods, people and information often requires simple speed-distance-time calculations, especially in Paper 2 skills questions.
理解货物、人员和信息的流动常常需要简单的速度-距离-时间计算，尤其在试卷二的技能题中。
Speed = Distance ÷ Time
速度 = 距离 ÷ 时间
Distance = Speed × Time
距离 = 速度 × 时间
Time = Distance ÷ Speed
时间 = 距离 ÷ 速度
Make sure units match: if speed is in km/h, distance should be in km and time in hours.
确保单位一致：若速度单位为公里/小时，距离应为公里，时间应为小时。
12. Map Scale, Area & Unit Conversions | 地图比例尺、面积与单位转换
Many IGCSE questions require working with map scales to calculate real-world distances and areas. Use the linear scale (line scale) or representative fraction (RF).
许多IGCSE考题要求运用地图比例尺计算实际距离和面积。可使用线段比例尺或分数比例尺（RF）。
Real Distance = Map Distance × Scale Factor
实际距离 = 图上距离 × 比例尺倍数
For example, with a scale of 1:50,000, 1 cm on the map equals 50,000 cm (or 0.5 km) on the ground.
例如，比例尺为1:50,000时，图上1厘米代表实地50,000厘米（即0.5公里）。
Key Area Conversions | 关键面积换算
- 1 km² = 1,000,000 m²
- 1 hectare = 10,000 m²
- 1 km² = 100 hectares
To estimate the area of an irregular shape on a map, use the grid square method: count full squares and estimate partial squares. Then convert using the scale.
估算地图上不规则区域的面积时，使用方格法：数出完整方格并估算部分方格。再根据比例尺换算。
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