AS CAIE Geography: Formulas and Theorems Quick Reference Handbook | AS CAIE 地理：公式定理速查手册

📚 AS CAIE Geography: Formulas and Theorems Quick Reference Handbook | AS CAIE 地理：公式定理速查手册

This handbook compiles the essential formulas, models and laws you need to master for the Cambridge AS Level Geography syllabus. Use it as a quick reference to consolidate data-response skills, physical processes and human geography concepts.

本手册汇编了剑桥AS地理课程大纲所必需的关键公式、模型与定律。可将其用作快速参考，巩固数据分析技能、自然地理过程与人文地理概念。

1. Demographic Indicators Formulas | 人口指标公式

Crude Birth Rate (CBR) shows the number of live births per 1000 people in a given year. The formula is:

粗出生率（CBR）表示某年每千人中的活产婴儿数。公式如下：

CBR = (Number of live births ÷ Total population) × 1000

粗出生率 = (活产数 ÷ 总人口) × 1000

Crude Death Rate (CDR) measures deaths per 1000 people:

粗死亡率（CDR）衡量每千人中的死亡人数：

CDR = (Number of deaths ÷ Total population) × 1000

粗死亡率 = (死亡人数 ÷ 总人口) × 1000

Rate of Natural Increase (RNI) is the difference between births and deaths, often expressed as a percentage:

自然增长率（RNI）是出生与死亡之差，通常以百分数表示：

RNI (per 1000) = CBR − CDR

自然增长率（每千人）= CBR − CDR

RNI % = (CBR − CDR) ÷ 10

自然增长率 % = (CBR − CDR) ÷ 10

Infant Mortality Rate (IMR) reflects deaths of infants under one year per 1000 live births:

婴儿死亡率（IMR）反映每千例活产中一岁以下婴儿的死亡数：

IMR = (Deaths under 1 ÷ Live births) × 1000

婴儿死亡率 = (一岁以下死亡数 ÷ 活产数) × 1000

To estimate the years needed for a population to double, apply the Rule of 70:

估算人口翻一番所需的年数，可应用“70法则”：

Doubling time (years) = 70 ÷ Growth rate (%)

倍增时间（年）= 70 ÷ 增长率 (%)

The Dependency Ratio helps assess the pressure on the working-age population:

抚养比用于评估劳动年龄人口的负担压力：

Dependency Ratio = [(Population 0–14 + 65+) ÷ Population 15–64] × 100

抚养比 = [(0–14岁人口 + 65岁以上人口) ÷ 15–64岁人口] × 100

2. Migration and Urbanisation Formulas | 迁移与城市化公式

Net migration is the balance between immigrants and emigrants:

净迁移是迁入者与迁出者之间的差额：

Net Migration = Number of immigrants − Number of emigrants

净迁移 = 迁入人数 − 迁出人数

The Net Migration Rate standardises the figure per 1000 population:

净迁移率将数值标准化为每千人的指标：

Net Migration Rate = (Net Migration ÷ Total population) × 1000

净迁移率 = (净迁移 ÷ 总人口) × 1000

Urbanisation level indicates the proportion of people living in urban areas:

城市化水平表示居住在城镇地区的人口比例：

Urbanisation (%) = (Urban population ÷ Total population) × 100

城市化率 (%) = (城镇人口 ÷ 总人口) × 100

The Rate of Urbanisation measures how fast the urban share is changing annually:

城市化速率衡量城镇人口占比每年的变化快慢：

Rate of Urbanisation = (Urbanisation % in Year 2 − Urbanisation % in Year 1) ÷ Time (years)

城市化速率 = (第2年城市化% − 第1年城市化%) ÷ 时间（年）

3. River Discharge and Flow Formulas | 河流流量与流速公式

River discharge (Q) is the volume of water passing a cross-section per unit time. It is fundamental to fluvial studies:

河流流量（Q）是单位时间内通过某一横截面的水体体积，是河流研究的基础：

Q = A × V

流量 = 横截面积 × 平均流速

Q is measured in cubic metres per second (m³ s⁻¹), A is cross-sectional area in m², and V is mean velocity in m s⁻¹.

Q 以立方米每秒（m³ s⁻¹）为单位，A 为横截面积（m²），V 为平均流速（m s⁻¹）。

The Hydraulic Radius (R) is used to assess channel efficiency:

水力半径（R）用于评估河道效率：

R = A ÷ P

水力半径 = 横截面积 ÷ 湿周

where P is the wetted perimeter (the length of the bed and banks in contact with water). A larger hydraulic radius normally indicates a more efficient channel with less friction.

P 为湿周（河床与河岸与水接触的长度）。水力半径越大，通常表明河道效率越高，摩擦力越小。

Gradient is the steepness of a river channel:

河道比降是河流的陡峭程度：

Gradient = Vertical drop (m) ÷ Horizontal distance (km) [expressed as m/km]

比降 = 垂直高差 (m) ÷ 水平距离 (km) [以 m/km 表示]

4. Water Balance Equation | 水平衡方程

The water balance describes the movement of water within a drainage basin over a specific period. It is a core concept in hydrology:

水平衡描述了特定时段内流域的水量移动，是水文学的核心概念：

P = Q + E + ΔS

降水 = 径流 + 蒸发蒸腾 + 蓄水量变化

P is precipitation, Q is runoff (stream discharge), E is evapotranspiration, and ΔS is the change in storage (soil moisture, groundwater, lakes). All terms are often expressed in millimetres (mm) of water depth.

P 为降水量，Q 为径流量（河流流量），E 为蒸发蒸腾量，ΔS 为蓄水量变化（土壤水、地下水、湖泊）。所有项通常以水深毫米（mm）表示。

The runoff coefficient indicates what fraction of precipitation becomes quick flow:

径流系数表示降水中有多大比例转化为快速径流：

Runoff coefficient = Runoff (mm) ÷ Precipitation (mm)

径流系数 = 径流量 (mm) ÷ 降水量 (mm)

A value close to 1 suggests high surface runoff (urbanised or saturated ground), while a low coefficient indicates high infiltration.

系数接近1表示地表径流高（城市化或饱和地面），低系数则表示下渗量大。

5. Atmospheric Lapse Rates and Buys Ballot’s Law | 大气递减率与白贝罗定律

Understanding lapse rates is essential for explaining atmospheric stability and rainfall. Remember three key values:

理解递减率对解释大气稳定度与降水至关重要，请记住三个关键值：

Environmental Lapse Rate (ELR): average 6.5 °C per 1000 m
Dry Adiabatic Lapse Rate (DALR): 10 °C per 1000 m
Saturated Adiabatic Lapse Rate (SALR): ranging roughly from 5 °C to 7 °C per 1000 m

环境递减率（ELR）：平均每1000 m降温6.5 °C
干绝热递减率（DALR）：每1000 m降温10 °C
湿绝热递减率（SALR）：大致为每1000 m降温5 °C至7 °C

Conditional instability occurs when ELR lies between DALR and SALR, making the atmosphere unstable only if the air is saturated.

当ELR介于DALR与SALR之间时，出现条件性不稳定，即空气饱和时大气才变得不稳定。

Buys Ballot’s Law relates wind direction to pressure systems. In the Northern Hemisphere, if you stand with your back to the wind, low pressure is on your left. (In the Southern Hemisphere, low pressure is on your right.)

白贝罗定律将风向与气压系统关联起来。在北半球，若背风而立，低压在你左侧。（南半球，低压在你右侧。）

6. Bradshaw Model | 布拉德肖模型

The Bradshaw model is a conceptual framework that shows how channel characteristics change from source to mouth. Although not a mathematical formula, it is a critical diagrammatic theorem for AS fluvial geomorphology.

布拉德肖模型是一个概念性框架，展示河道特征从源头至河口的变化。虽非数学公式，却是AS河流地貌学中关键的图解定理。

Key trends predicted downstream:

Discharge increases
Mean velocity increases
Hydraulic radius increases
Channel depth and width increase
Bedload particle size decreases
Channel gradient decreases

预测的下游趋势：

流量增大
平均流速增大
水力半径增大
河道深度与宽度增大
推移质粒径减小
河道比降减小

The model also plots changes in load quantity and the competence of the river. Use it to answer questions on downstream changes and flood risks.

该模型还描绘了搬运物数量及河流搬运能力的变化。可用来回答有关下游变化与洪水风险的问题。

7. Hjulström Curve | 希尤斯特龙曲线

The Hjulström curve is a fundamental geomorphic theorem that relates particle size to the critical velocities needed for erosion, transport and deposition. It is widely examined.

希尤斯特龙曲线是一条重要的地貌定理，将粒径与侵蚀、搬运、沉积所需的临界流速联系起来，常出现在考题中。

The curve shows a U-shaped erosion zone: cohesive clays and silts require higher velocities to entrain than fine sands because of cohesion.
The lowest erosion velocity is for particles around 0.1–0.5 mm (sand).
Once in motion, particles can be transported at much lower velocities than those needed for erosion.
When velocity drops below the fall velocity, deposition occurs.

曲线呈U形侵蚀带：黏土和粉砂因黏结性，起动所需流速高于细沙。
侵蚀流速最低的颗粒粒径约为0.1–0.5 mm（砂）。
一旦进入运动，颗粒可在远低于侵蚀流速的流速下被搬运。
当流速降至沉降速度以下时，发生沉积。

Apply the Hjulström curve to explain why sand is often found in suspension, and why clay banks remain stable in slow currents but erode during floods.

应用希尤斯特龙曲线可以解释为何砂常以悬移质出现，为何黏土岸在缓流中保持稳定却在洪水时受到侵蚀。

8. Ravenstein’s Laws of Migration | 拉文斯坦移民法则

E. G. Ravenstein’s laws of migration (1885) remain a cornerstone for explaining migration patterns. The key ‘laws’ are empirical generalisations:

雷文斯坦的移民法则（1885年）至今仍是解释迁移模式的基石。这些“法则”是经验性的概括：

Most migrants move only a short distance (step migration).
Long-distance migrants head towards major industrial and commercial centres.
Each current of migration produces a counter-flow.
Rural dwellers are more migratory than urban dwellers.
Women are more migratory than men within their own country, but men dominate international migration.
Large towns grow more by migration than by natural increase.
Economic factors are the prime cause of migration.

大多数迁移者只进行短距离迁移（逐步迁移）。
长距离迁移者前往主要的工商业中心。
每一股迁移流都会产生相应的反向流。
农村居民比城市居民更易迁移。
在国内迁移中女性多于男性，而在国际迁移中男性占主导。
大城市更多依靠迁移而非自然增长来壮大。
经济因素是引发迁移的首要原因。

9. Demographic Transition Model (DTM) | 人口转变模型（DTM）

The Demographic Transition Model links population change to economic development. It describes a sequence of five stages through which birth and death rates change, altering total population size.

人口转变模型将人口变化与经济发展联系起来，描述了出生率和死亡率经历五个阶段的变化，从而引起总人口规模的改变。

Stage / 阶段	Birth Rate / 出生率	Death Rate / 死亡率	Natural Change / 自然变化
1 Traditional / 传统社会	High / 高	High / 高	Low, fluctuates / 低且波动
2 Expanding / 扩张期	High / 高	Falling / 下降	High increase / 高增长
3 Late expanding / 后期扩张	Falling / 下降	Low / 低	Slowing increase / 增长放缓
4 Low fluctuating / 低平稳	Low / 低	Low / 低	Stable or very slow / 稳定或极缓
5 Decline? / 衰退?	Very low / 极低	Low, may rise / 低，可能上升	Negative / 负增长

Use the DTM to explain population pyramids, dependency changes and the shift from agricultural to industrial societies.

运用DTM可解释人口金字塔、抚养比变化以及从农业社会向工业社会的转型。

10. Coriolis Force and Wind Deflection | 科里奥利力与风偏转

The Coriolis force arises from the Earth’s rotation and causes moving air and water to deflect. It is not a formula per se, but its effects are essential for global atmospheric circulation and pressure systems.

科里奥利力由地球自转产生，使运动中的空气和水发生偏转。其本身不是公式，但对全球大气环流与气压系统至关重要。

Northern Hemisphere: deflection to the right
Southern Hemisphere: deflection to the left
Coriolis force increases with latitude (zero at the equator, maximum at the poles) and with wind speed.

北半球：向右偏转
南半球：向左偏转
科里奥利力随纬度增高而增大（赤道为零，两极最大），并随风速增大而增强。

This deflection explains the formation of trade winds, westerlies and polar easterlies. It also underpins the spiral patterns of tropical cyclones and ocean currents.

这一偏转解释了信风、西风带和极地东风带的形成，也是热带气旋和洋流螺旋路径的原因。

Wind direction control = Pressure gradient force + Coriolis force + Friction

风向控制 = 气压梯度力 + 科里奥利力 + 摩擦力

Geostrophic wind is the balance between pressure gradient force and Coriolis force, blowing parallel to isobars at high altitudes.

地转风是气压梯度力与科里奥利力平衡的结果，在高空沿等压线平行吹送。

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AS CAIE Geography: Formulas and Theorems Quick Reference Handbook | AS CAIE 地理：公式定理速查手册