📚 Geography Formula & Key Concepts Quick Reference Handbook | 地理公式与关键概念速查手册
This reference compiles the most essential calculations and numerical relationships encountered in the Cambridge AS Geography syllabus. Mastering these formulae supports accurate data interpretation in both Physical and Human Geography, from population change to river discharge.
本手册汇总了剑桥AS地理课程中最关键的计算与数值关系。掌握这些公式有助于在自然地理和人文地理中准确解读数据，从人口变化到河流流量。
1. Natural Increase Rate | 自然增长率
Natural increase is the bedrock of demographic analysis. It expresses the percentage by which a population grows or declines in a year, excluding net migration.
自然增长是人口分析的基础。它表示一年内人口增长或下降的百分比，不包括净迁移。
Natural Increase Rate (%) = (Birth Rate − Death Rate) / 10
自然增长率(%) = (出生率 − 死亡率) / 10
Birth and death rates are given per 1000 people per year. Dividing by 10 converts the result into a percentage.
出生率和死亡率以每年每千人为单位。除以10可将结果转换为百分比。
2. Doubling Time (Rule of 70) | 人口倍增时间 (70法则)
A quick estimate of the years required for a population to double, assuming constant exponential growth.
快速估算人口翻一番所需的年数，假设持续指数增长。
Doubling Time (years) ≈ 70 / Growth Rate (%)
倍增时间(年) ≈ 70 / 增长率(%)
The growth rate here is the natural increase rate (or total growth rate if net migration is small). For a growth rate of 2%, doubling takes about 35 years.
此处的增长率指自然增长率（或总增长率，若净迁移量很小）。若增长率为2%，倍增约需35年。
3. Population Density | 人口密度
Population density measures the concentration of people in a defined area, highlighting spatial variations in human settlement.
人口密度衡量一定区域内人口的集中程度，反映人类聚落的空间差异。
Population Density = Total Population / Total Land Area (km² or hectare)
人口密度 = 总人口 / 土地总面积 (平方公里或公顷)
Always state the unit, e.g. people per km². Agricultural density (farmers per unit of arable land) and physiological density (people per unit of arable land) are useful derivatives.
务必注明单位，例如每平方公里人数。农业密度(单位耕地面积上的农民数)和生理密度(单位耕地面积上的人口数)是有用的衍生指标。
4. Urbanisation Level | 城市化水平
Urbanisation level quantifies the share of a country’s population living in areas classified as urban.
城市化水平量化了一个国家居住在被归类为城市地区的人口比例。
Urbanisation Level (%) = (Urban Population / Total Population) × 100
城市化水平(%) = (城市人口 / 总人口) × 100
Different countries define ‘urban’ differently (e.g. settlement size above 2000 people). Be aware of the definition when comparing data.
不同国家对“城市”的定义不同(例如超过2000人的聚落)。比较数据时需注意定义。
5. Rate of Urbanisation | 城市化速率
This measures how fast the urban share of the total population is changing over time.
该指标衡量城市人口占总人口比例随时间的变化速度。
Rate of Urbanisation (%) = Change in Urban Population Proportion / Time Period (years)
城市化速率(%) = 城市人口比例的变化量 / 时间跨度(年)
Often presented as percentage points per year. High rates are typical of rapidly industrialising economies.
通常以每年百分点表示。高速率是快速工业化经济体的典型特征。
6. River Discharge | 河流流量
Discharge is the volume of water passing a cross-section of a river per unit time. It is fundamental to flood and water resource studies.
流量是单位时间内通过河流横断面的水量，是洪水和水资源研究的基础。
Q = A × V
流量 (Q) = 横截面积 (A) × 平均流速 (V)
- Q in cubic metres per second (m³/s) or cumecs, A in m², V in m/s.
- Q 单位是立方米/秒(或cumec)，A 是平方米，V 是米/秒。
Velocity is measured with a flowmeter; cross-sectional area is calculated by multiplying channel width by mean depth.
流速用流速仪测量；横截面积由河道宽度乘以平均深度计算得出。
7. Drainage Density | 排水密度
Drainage density reflects the efficiency of a basin’s drainage system and its landscape dissection.
排水密度反映流域排水系统的效率及地形切割程度。
Drainage Density = Total Stream Length (km) / Drainage Basin Area (km²)
排水密度 = 河流总长度 (公里) / 流域面积 (平方公里)
High drainage density (many channels per unit area) indicates impermeable surface, steep slopes or limited vegetation; low density characterises permeable, vegetated basins.
高排水密度(单位面积内河道多)表明地表不透水、坡度陡或植被稀疏；低密度则常见于渗透性好、植被茂密的流域。
8. Stream Gradient | 河道梯度
Gradient describes the steepness of a river channel, which influences flow velocity and erosive power.
梯度描述河道陡峭程度，影响流速和侵蚀力。
Gradient = Vertical Fall (m) / Horizontal Distance (m)
梯度 = 垂直落差 (米) / 水平距离 (米)
Expressed as a ratio (e.g. 1:50) or as metres per kilometre. Gradient typically decreases downstream, forming a concave long profile.
可用比例(如1:50)或每公里的米数表示。梯度通常向下游递减，形成凹形纵剖面。
9. Storm Hydrograph Metrics | 暴雨水文过程线指标
Hydrograph analysis uses several variables to interpret a river’s response to a rainfall event.
水文过程线分析使用多个变量来解释河流对降雨事件的响应。
Peak Discharge (m³/s), Lag Time (hours), Rising Limb, Falling Limb
洪峰流量(立方米/秒)、滞后时间(小时)、涨水段、退水段
- Lag time = time between peak rainfall and peak discharge.
- 滞后时间 = 降雨峰值与流量峰值之间的时间间隔。
- Base flow = groundwater contribution; storm flow = surface runoff + throughflow.
- 基流 = 地下水补给；暴雨径流 = 地表径流 + 壤中流。
Short lag time and high peak discharge suggest flashy behaviour, typical of urban or deforested catchments.
滞后时间短、洪峰流量高表明暴涨暴落的特性，常见于城市化或森林砍伐的流域。
10. Rainfall–Runoff Relationship | 降雨–径流关系
The runoff coefficient helps evaluate what proportion of rainfall becomes stream flow.
径流系数有助于评估降雨转化为河川径流的比例。
Runoff Coefficient = Runoff Volume (m³) / Total Rainfall Volume (m³)
径流系数 = 径流总量 (立方米) / 降雨总量 (立方米)
The ratio varies between 0 and 1. Impervious surfaces give coefficients close to 1; permeable soil and forest cover give lower values.
该比值介于0到1之间。不透水表面的系数接近1；渗透性土壤和森林覆盖的系数较低。
11. Dependency Ratio | 抚养比率
The dependency ratio indicates the pressure on the productive population to support the young and old.
抚养比率表示劳动年龄人口抚养少儿和老年人的压力。
Age Dependency Ratio (%) = [(Population 0–14 + Population 65+) / Population 15–64] × 100
年龄抚养比 (%) = [(0–14岁人口 + 65岁以上人口) / 15–64岁人口] × 100
Youth dependency and old-age dependency can be separated. High ratios in developing countries reflect large youth populations; in ageing societies, old-age dependency dominates.
少儿抚养比和老年抚养比可以分开计算。高抚养比在发展中国家反映大量年轻人；在老龄化社会，老年抚养比占主导。
12. Net Migration Rate | 净迁移率
Net migration captures the balance between immigration and emigration, which is crucial for understanding population change alongside natural increase.
净迁移反映迁入与迁出的平衡，对于理解伴随自然增长的人口变化至关重要。
Net Migration Rate (per 1000) = [(Immigrants − Emigrants) / Mid-year Population] × 1000
净迁移率 (每千人) = [(迁入人数 − 迁出人数) / 年中人口] × 1000
A positive value means net in-migration; a negative value means net out-migration. Combine with natural increase to obtain total population growth rate.
正值表示净迁入；负值表示净迁出。结合自然增长率可得到总人口增长率。
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