📚 IGCSE Cambridge Geography: Formula & Theorem Quick Reference Handbook | IGCSE 剑桥地理：公式定理速查手册
This handbook brings together the essential formulae, calculations and key relationships you will need for the Cambridge IGCSE Geography examination. Each entry is presented with a clear English explanation followed by a matching Chinese translation, making it easy to revise and apply in both structured questions and data-response tasks.
本手册汇集了剑桥 IGCSE 地理考试所需的基本公式、计算方法与关键关系。每个条目先提供清晰的英文解释，再配上对应的中文翻译，便于在结构化问题与数据分析题中灵活运用。
1. Map Scale & Distance Calculations | 地图比例尺与距离计算
la is: Actual distance = map distance × scale denominator. For example, on a 1:50,000 map, 1 cm represents 50,000 cm, i.e. 0.5 km. Curved distances can be measured with a piece of string or an opisometer.
在地形图上，距离通过测量图上直线或曲线长度并按比例尺换算得到。公式为：实际距离 = 图上距离 × 比例尺分母。例如，在 1:50,000 地图上，1 厘米代表 50,000 厘米，即 0.5 公里。曲线距离可用细线或量距器测量。
| Term | Formula / Meaning |
|---|---|
| Straight-line distance | dactual = dmap × S (S = scale factor, e.g. 50,000) |
| Area (regular shape) | A = length × width on ground (both converted from map) |
| Grid square area | 1 km × 1 km = 1 km² if grid lines represent 1 km spacing |
2. Gradient & Cross-Section Area | 坡度与横截面积
h as 1:10 or as a percentage. Formula: Gradient = VI ÷ HE (both in same units). Cross-section area is used for river channel shape and is commonly treated as a trapezium: Area = ½ × (a + b) × d where a and b are top and bottom widths and d is depth.
坡度表示陡峭程度，以垂直落差 (VI) 与水平距离 (HE) 之比表示，常简化为 1:10 等形式或百分比。公式：坡度 = VI ÷ HE（单位统一）。河流横截面积常用梯形近似：面积 = ½ × (a + b) × d，其中 a 和 b 为上下宽，d 为深度。
| Gradient | G = VI / HE; VI = difference in height (m); HE = horizontal distance (m) |
|---|---|
| Gradient ratio | 1:(HE/VI) |
| Percentage gradient | (VI/HE) × 100% |
3. Latitude & Longitude: Time Difference | 经纬度与时差计算
h Mean Time (GMT); places west are behind. Formula: Time difference = (difference in longitude ÷ 15) hours. For every 1° longitude difference, time changes by 4 minutes.
地球自转 360° 需 24 小时，因此每 15° 经度对应 1 小时时差。本初子午线以东的地方比格林威治标准时间 (GMT) 早，以西的地方晚。公式：时差 = (经度差 ÷ 15) 小时。经度每相差 1°，时间相差 4 分钟。
Time difference (h) = Δλ ÷ 15°
1° longitude → 4 minutes
4. Population Density & Distribution | 人口密度与分布
lly expressed in persons per km². Formula: Density = population ÷ area (km²). Population distribution describes the spread of people and can be shown as dot maps or choropleth maps.
人口密度衡量一个地区的拥挤程度，用总人口除以土地总面积得到，单位通常为人/平方公里。公式：密度 = 人口 ÷ 面积（平方公里）。人口分布描述人口的空间集聚形态，常用点值图或等值区域图表示。
| Population density | D = P / A (P = population, A = area in km²) |
| Physiological density | Dphys = population ÷ arable land area |
5. Crude Birth Rate, Crude Death Rate & Natural Increase | 粗出生率、粗死亡率与自然增长率
0. Crude Death Rate (CDR) = (number of deaths ÷ total population) × 1000. Units are per 1000 people per year. Natural increase rate (NIR) = (CBR – CDR) / 10, expressed as a percentage. The formula: NIR (%) = (CBR – CDR) ÷ 10.
这些人口指标是理解人口变化的关键。粗出生率 (CBR) = (活产婴儿数 ÷ 总人口) × 1000；粗死亡率 (CDR) = (死亡人数 ÷ 总人口) × 1000，单位是每千人每年。自然增长率 (NIR) = (CBR – CDR) ÷ 10，以百分比表示。
CBR (‰) = (live births ÷ total pop.) × 1000
CDR (‰) = (deaths ÷ total pop.) × 1000
NIR (%) = (CBR – CDR) ÷ 10
6. Total Fertility Rate & Dependency Ratio | 总和生育率与抚养比
ve levels. The dependency ratio shows the burden on the working-age population. Young dependency ratio = (population aged 0–14 ÷ population aged 15–64) × 100. Old dependency ratio = (population aged 65+ ÷ population aged 15–64) × 100. Total dependency ratio = sum of young and old ratios.
总和生育率 (TFR) 是平均每个妇女一生生育的孩子数，用于比较生育水平。抚养比反映劳动年龄人口的负担。少儿抚养比 = (0–14 岁人口 ÷ 15–64 岁人口) × 100；老年抚养比 = (65 岁及以上人口 ÷ 15–64 岁人口) × 100；总抚养比 = 少儿抚养比 + 老年抚养比。
| Youth dep. ratio | (Pop 0-14 ÷ Pop 15-64) × 100 |
| Old dep. ratio | (Pop 65+ ÷ Pop 15-64) × 100 |
| Total dep. ratio | Youth + Old |
7. Urbanisation Rate & Rural-Urban Migration | 城市化率与城乡迁移
Urbanisation rate measures the proportion of a country's population living in urban areas. Formula: Urban population (% nnual change in this percentage. Key migration formulas include net migration = immigrants – emigrants. Push-pull factors explain rural-to-urban movement.
城市化率衡量国家人口中居住在城市地区的比例，公式：城市人口比例 = (城市人口 ÷ 总人口) × 100。城市化速度是该比例的年度变化量。重要迁移公式有净迁移量 = 迁入人口 – 迁出人口。推拉因素解释乡城迁移。
| Urban % | (Urban pop. / Total pop.) × 100 |
| Net migration | I – E (immigrants minus emigrants) |
| Rural depopulation | Often calculated as % loss over time |
8. Hydrological Cycle: Discharge & Base Flow | 水文循环：流量与基流
s discharge (m³/s), A is cross-sectional area (m²) and v is mean velocity (m/s). Base flow is the portion of streamflow that comes from groundwater seepage. Storm flow plus base flow equals total discharge, shown on a hydrograph.
河流流量是单位时间内通过横截面的水量，公式：Q = A × v，其中 Q 为流量 (m³/s)，A 为横截面积 (m²)，v 为平均流速 (m/s)。基流是来自地下水渗流的径流部分。暴雨径流加基流等于总流量，在水文过程线上显示。
Q (discharge, m³/s) = A × v
Total flow = Stormflow + Baseflow
9. Climate: Temperature Range & Precipitation Variability | 气候：气温较差与降水量变率
hest and lowest monthly mean temperatures. Annual temperature range = maximum monthly mean – minimum monthly mean. Diurnal range = daytime max – ficient of variation: (standard deviation of annual rainfall ÷ mean annual rainfall) × 100%, or simply the range between wet and dry years.
气温较差是月平均最高温与最低温的差值。年较差 = 最热月均温 – 最冷月均温；日较差 = 白天最高温 – 夜间最低温。降水变率可用变异系数表示：(年降水量标准差 ÷ 多年平均降水量) × 100%，或直接用最湿年与最干年的差值计算。
| Annual temp. range | Tmax (month mean) – Tmin (month mean) |
| Diurnal range | Day max – Night min |
| Rainfall variability | (Highest annual total – Lowest) or CV (%) |
10. Economic Indicators: GDP per Capita & HDI | 经济指标：人均GDP与人类发展指数
c Product ÷ population. It is often given in US dollars. The Human Development Index (HDI) combines life expectancy, education (mean and expected years of schooling) and GNI per capita into a single index between 0 and 1. The geometric mean of the three normalised indices is used. Understanding these indicators is essential for development geography.
人均 GDP 是反映人均经济产出的指标，公式：人均 GDP = 国内生产总值 ÷ 人口，通常以美元计。人类发展指数 (HDI) 将预期寿命、教育（平均受教育年限与预期受教育年限）以及人均国民总收入综合为一个 0 至 1 之间的单一指数，采用三个标准化指数的几何平均值。理解这些指标对发展地理学至关重要。
HDI = ³√(Ilife × Ieducation × Iincome)
Note: GNI per capita is now used instead of GDP for HDI calculation, but GDP per capita is still a common comparative measure.
注：HDI 计算中目前使用人均国民总收入而非 GDP，但人均 GDP 仍是常用比较指标。
11. Environmental Footprint & Carrying Capacity | 生态足迹与环境承载力
s and to absorb its wastes. It is expressed in global hectares per person (gha). The formula for overshoot: ecological deficit = footprint – Carrying capacity is the maximum population size an environment can sustain indefinitely.
生态足迹衡量一个群体生产所消费的资源以及吸收其废弃物所需的生物生产性土地与水域面积，单位为人均全球公顷 (gha)。当足迹超过生物承载力时，生态赤字 = 足迹 – 承载力。环境承载力是环境可持续支撑的最大人口规模。
| Ecological deficit | Footprint (gha/cap) – Biocapacity (gha/cap) |
| Carrying capacity | Influenced by technology, lifestyle, resource use |
12. Population Pyramids & Projections | 人口金字塔与预测
A population pyramid is a bar chart showing the age and sex structure of a population. It allows quick calculation of the youth, working-age and elderly cohorts. The percentage of each cohort helps estimate dependency ratios. Projecting future population uses the formula: Pfuture = Ppresent × (1 + r)t ual growth rate (as a decimal) and t = number of years. Doubling time ≈ 70 ÷ growth rate (% per year).
人口金字塔是显示人口年龄与性别结构的条形图，可快速估算少儿、劳动年龄与老年人口比例。各队列百分比用于计算抚养比。预测未来人口采用公式：P未来 = P现在 × (1 + r)t，其中 r 为年增长率（小数），t 为年数。翻倍时间 ≈ 70 ÷ 年增长率 (%).
Pt = P0 (1 + r)t
Doubling time (years) ≈ 70 ÷ r (%)
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