KS3 CIE Geography: Quick Reference Handbook of Formulas and Theorems | KS3 CIE 地理：公式定理速查手册

📚 KS3 CIE Geography: Quick Reference Handbook of Formulas and Theorems | KS3 CIE 地理：公式定理速查手册

This handbook provides a concise collection of essential formulas, models and calculation techniques required for the KS3 CIE Geography course. Mastering these tools will help you interpret maps, analyse population data, understand river dynamics and explain key geographical patterns. Each section pairs an English explanation with its Chinese translation, ensuring clarity for bilingual learners.

本手册汇总了 KS3 CIE 地理课程必备的核心公式、模型与计算技巧。掌握这些工具将帮助你解读地图、分析人口数据、理解河流动态并解释关键地理格局。每个部分均提供中英文对照讲解，确保双语学习者能够清晰理解。

1. Map Scale | 地图比例尺

Map scale shows the relationship between a distance on a map and the corresponding distance on the ground. It can be expressed as a statement (e.g., 1 cm represents 1 km), a representative fraction (e.g., 1:100 000), or a linear bar scale.

地图比例尺表示图上距离与实地距离之间的关系。它可以用文字式（如 1 厘米代表 1 公里）、分数式（如 1:100 000）或直线比例尺来表示。

The formula for converting map distance to real-world distance is:

将图上距离转换为实际距离的公式为：

Actual Distance (km) = Map Distance (cm) × Scale Denominator ÷ 100 000

实际距离（公里）= 图上距离（厘米）× 比例尺分母 ÷ 100 000

For a 1:50 000 map, every 1 cm on the map equals 50 000 cm (0.5 km) on the ground. Always check the scale before measuring distances or calculating areas.

对于 1:50 000 的地图，图上每 1 厘米代表实地 50 000 厘米（0.5 公里）。在测量距离或计算面积之前，务必核对比例尺。

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2. Measuring Straight and Curved Distances | 测量直线与曲线距离

Straight-line distances are measured with a ruler and then converted using the map scale. Curved distances, such as a river or road, require a piece of string or a pair of dividers to follow the twists, after which the string length is measured against the ruler.

直线距离用直尺测量，再根据地图比例尺换算。曲线距离（如河流或道路）需要用细绳或分规沿弯曲路径贴合，然后将绳长用直尺量出为准。

For example, if your string measures 12.4 cm on a 1:25 000 map, the actual distance is:

例如，如果细绳在 1:25 000 地图上测得长度为 12.4 厘米，则实际距离为：

Distance = 12.4 × 25 000 ÷ 100 000 = 3.1 km

距离 = 12.4 × 25 000 ÷ 100 000 = 3.1 公里

When measuring curved routes, take the measurement twice to improve accuracy.

测量曲折路线时，应重复测量两次以提高准确性。

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3. Area Calculation | 面积计算

Area on a map can be estimated using grid squares. On many topographic maps, each grid square represents a known ground area (e.g., 1 km² when the grid lines are 1 km apart).

地图上的面积可以通过网格来估算。许多地形图上，每个网格代表已知的实际面积（例如网格间距为 1 公里时，每格代表 1 平方公里）。

To calculate area, count the number of full squares and combine partial squares to estimate the total number of complete squares. Then apply the formula:

计算面积时，先数出完整网格的数量，再将不完整的部分拼凑成完整网格进行估算。然后应用公式：

Area (km²) = Number of Squares × Area represented by one square (km²)

面积（平方公里）= 网格数 × 每个网格代表的面积（平方公里）

For irregular shapes you can also use the rectangle method or overlay tracing paper with a dot grid to improve accuracy.

对于不规则形状，还可以采用矩形法，或使用带有点阵的透明描图纸来提升精度。

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4. Gradient | 坡度计算

Gradient describes the steepness of a slope. It is expressed as the ratio of vertical rise to horizontal distance, often written as ‘1 in n’ where n is the horizontal distance needed to rise by one unit.

坡度描述斜坡的陡峭程度。它表示为垂直高度与水平距离的比值，通常写成“1 in n”，其中 n 是每上升一个单位高度所需的水平距离。

Gradient = Vertical difference (m) ÷ Horizontal distance (m)

坡度 = 垂直高差（米） ÷ 水平距离（米）

If a hill rises 80 m over a horizontal distance of 400 m, the gradient is:

如果一座山丘水平距离 400 米，上升了 80 米，则坡度为：

80 ÷ 400 = 0.2 or 1 in 5

80 ÷ 400 = 0.2 或 1 in 5

Steep gradients have a small number after ‘1 in’ (e.g., 1 in 3 is steeper than 1 in 10).

“1 in”后面的数字越小，坡度越陡（如 1 in 3 比 1 in 10 更陡）。

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5. Population Density | 人口密度

Population density measures how crowded an area is. It helps geographers compare how people are distributed between different regions.

人口密度衡量一个地区的拥挤程度，有助于地理学家比较不同区域的人口分布状况。

Population Density = Total population ÷ Land area (km²)

人口密度 = 总人口 ÷ 土地面积（平方公里）

For example, if a country has 5 million people and an area of 100 000 km², its population density is 50 people per km². High densities are typical in cities and fertile river valleys, while deserts and mountains tend to have low densities.

例如，某国人口 500 万，面积 10 万平方公里，则人口密度为 50 人/平方公里。高密度常见于城市和肥沃的河谷，而沙漠和山区往往密度较低。

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6. Birth Rate, Death Rate and Natural Increase | 出生率、死亡率与自然增长率

These demographic indicators show how a population is changing naturally, excluding migration. They are usually expressed per 1000 people per year.

这些人口指标反映在排除迁移因素后，人口是如何自然变化的。它们通常以每年每千人的数量来表示。

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

粗出生率 = （活产婴儿数 ÷ 总人口）× 1000

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

粗死亡率 = （死亡人数 ÷ 总人口）× 1000

The rate of natural increase (RNI) is found without multiplying by 1000, often converted to a percentage:

自然增长率（RNI）的计算无需再乘以 1000，常转换为百分比：

Natural Increase = (CBR – CDR) ÷ 10 (%)

自然增长率 = （出生率 – 死亡率） ÷ 10 （%）

A positive natural increase means the population is growing; a negative value signals natural decrease.

自然增长率为正表示人口在增长，为负则表示人口自然减少。

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7. Migration and Net Migration Rate | 迁移与净迁移率

Migration is the movement of people from one place to another. Net migration considers both immigration (people moving in) and emigration (people moving out).

迁移是指人们从一个地方移动到另一个地方。净迁移同时考虑迁入和迁出的人员。

Net Migration = Number of immigrants – Number of emigrants

净迁移 = 迁入人数 – 迁出人数

The net migration rate is expressed per 1000 people to allow comparisons:

净迁移率以每千人的形式表达，以便进行比较：

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

净迁移率 = （净迁移 ÷ 总人口）× 1000

When combined with natural increase, total population change can be calculated:

结合自然增长，可以计算总人口变化：

Population Change = (Births – Deaths) + (Immigration – Emigration)

人口变化 = （出生人数 – 死亡人数）+ （迁入人数 – 迁出人数）

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8. River Discharge | 河流流量

River discharge is the volume of water flowing through a river cross-section per unit time, usually measured in cubic metres per second (cumecs). It increases downstream as tributaries join.

河流流量是指单位时间内流过河道横截面的水体积，通常以立方米/秒（cumecs）为单位。受支流汇入影响，下游流量增大。

Discharge (m³/s) = Cross-sectional area (m²) × Average velocity (m/s)

流量（立方米/秒）= 横截面积（平方米）× 平均流速（米/秒）

Cross-sectional area is width multiplied by mean depth. Velocity can be measured with a flow meter or by timing a float. Understanding discharge helps predict flood risks and manage water resources.

横截面积等于河宽乘以平均水深。流速可用流速仪或浮标计时法测定。了解流量有助于预测洪水风险和管理水资源。

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9. Drainage Density | 排水密度

Drainage density describes how closely spaced the stream channels are in a drainage basin. It reflects the landscape’s ability to drain water and is influenced by climate, rock permeability and vegetation.

排水密度描述流域内河道分布的疏密程度。它反映地形排水能力，受气候、岩石透水性和植被的影响。

Drainage Density = Total length of all streams (km) ÷ Drainage basin area (km²)

排水密度 = 所有河道总长度（公里） ÷ 流域面积（平方公里）

A high drainage density (e.g., above 2 km/km²) often indicates impermeable rocks, steep slopes or sparse vegetation, which encourage rapid surface runoff. Low drainage density suggests permeable ground where water infiltrates easily.

高排水密度（例如大于 2 公里/平方公里）通常表明岩石透水性差、坡度陡或植被稀疏，促使地表径流快速形成。低排水密度则意味着地面渗透性强，水分易于下渗。

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10. Rainfall and Temperature Calculations | 降雨量与温度计算

Climatic data calculation is a fundamental skill. Annual rainfall totals and temperature ranges are used to construct climate graphs and compare climates.

气候数据计算是一项基本技能。年降雨总量和温度较差用于绘制气候图表和比较气候。

Total Annual Rainfall = Sum of monthly rainfall totals

年总降雨量 = 各月降雨量之和

Mean Annual Temperature = Sum of 12 monthly mean temperatures ÷ 12

年平均温度 = 12 个月平均温度之和 ÷ 12

Annual Temperature Range = Maximum monthly mean – Minimum monthly mean

年温差 = 最热月平均温度 – 最冷月平均温度

A large annual range indicates a continental climate, while a small range suggests a maritime or equatorial location.

年温差大表明为大陆性气候，而年温差小则暗示海洋性或赤道地区的位置。

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

The DTM is a theoretical model that describes how a country’s population changes over time as it develops. It consists of five stages, each defined by the relationship between birth rate, death rate and total population.

人口转变模型是一个理论模型，描述一个国家在发展过程中人口如何随时间变化。它分为五个阶段，每个阶段由出生率、死亡率和总人口之间的关系来定义。

Stage	Birth Rate	Death Rate	Natural Increase	Example
1 (High Stationary)	High	High	Very low	None today
2 (Early Expanding)	High	Falls rapidly	High	Afghanistan
3 (Late Expanding)	Falling	Low	Slowing	India
4 (Low Stationary)	Low	Low	Very low	UK
5 (Declining)	Very low	Low	Negative	Japan

The model helps explain changes in population structure, such as the shape of population pyramids, but it must be applied carefully as not all countries follow the exact sequence.

该模型有助于解释人口结构的变化，例如人口金字塔的形状，但需谨慎应用，因为并非所有国家都严格遵循这一序列。

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12. The Push-Pull Theory of Migration | 迁移的推拉理论

This theory explains why people migrate by dividing factors into push factors (reasons to leave an area) and pull factors (reasons to move to a destination).

该理论通过将因素划分为推因素（离开某地的原因）和拉因素（迁往某地的原因）来解释人们为何迁移。

Push factors include unemployment, war, poor services, crop failure and natural disasters. Pull factors include job opportunities, better healthcare, safer environment and higher living standards.

推因素包括失业、战争、公共服务差、作物歉收和自然灾害。拉因素包括就业机会、更好的医疗保健、更安全的环境和更高的生活水平。

A real migration flow is often the result of a combination of push and pull forces. For example, a farmer might be pushed by drought and pulled by the promise of urban employment. The theory is widely used to analyse rural-to-urban migration and international movements.

真实的迁移往往是推力和拉力共同作用的结果。例如，一位农民可能因干旱被推离，同时又受到城市就业前景的拉引。该理论广泛用于分析城乡迁移及国际人口流动。

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13. The Water Balance Equation | 水平衡方程

The water balance, or hydrological balance, describes how water moves through a drainage basin. It is a conservation equation showing the relationship between inputs and outputs of water.

水平衡或水文平衡描述了水在流域中的运动方式。它是一个水量守恒方程，展示水分的输入与输出之间的关系。

P = Q + E + ΔS

降水量 = 径流量 + 蒸散发量 + 储水量变化

where P is precipitation, Q is stream runoff, E is evapotranspiration (evaporation + transpiration) and ΔS is the change in water stored in soil, rock and lakes. Over a long period, ΔS tends to zero, so P = Q + E. This formula helps geographers understand why some rivers have high flow even during dry periods, and how deforestation can alter the balance.

其中 P 为降水量，Q 为河流径流量，E 为蒸散发量（蒸发 + 植物蒸腾），ΔS 为土壤、岩石和湖泊中储水量的变化。在较长时间尺度上，ΔS 趋近于零，因此 P = Q + E。该公式有助于理解为何某些河流在干旱期仍保持高流量，以及森林砍伐如何改变平衡。

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