KS3 Edexcel Geography: Formula and Theorem Quick Reference Handbook | KS3 Edexcel 地理：公式定理速查手册

📚 KS3 Edexcel Geography: Formula and Theorem Quick Reference Handbook | KS3 Edexcel 地理：公式定理速查手册

This quick reference handbook gathers all the key formulas, calculations, and geographic ‘theorems’ that you are expected to master at KS3 Edexcel Geography. From map skills to population change, these tools will help you interpret data, compare places, and answer exam questions with confidence. Keep this guide close – quick bites of essential knowledge, paired in English and Chinese, to speed up your revision.

本速查手册汇聚了 KS3 Edexcel 地理课程中你需要掌握的所有关键公式、计算方法和地理“定理”。从地图技能到人口变化，这些工具能帮助你解读数据、比较地区差异，并自信地应对考试题目。请随身携带这份指南——中英对照的精华知识点，助你高效复习。

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1. Map Scale and Distance Calculations | 地图比例尺与距离计算

Scale is the relationship between a distance on the map and the corresponding distance on the ground. The three ways to show scale are: as a ratio (1:50,000), as a statement (1 cm to 0.5 km), and as a linear (graphic) scale bar.

比例尺是地图上的距离与实地相应距离的比率。三种表示比例尺的方法：比例式（1:50,000）、文字式（1厘米代表0.5公里）、直线比例尺（图示比例尺）。

The most useful formula: Real Distance = Map Distance × Scale Factor. For a 1:25,000 map, 1 cm on the map equals 25,000 cm (or 0.25 km) on the ground. To convert from centimetres to kilometres, divide by 100,000.

最常用的公式：实地距离 = 图上距离 × 比例尺系数。在 1:25,000 地图上，图上 1 厘米等于实地 25,000 厘米（即 0.25 公里）。从厘米换算成公里，需除以 100,000。

Formula / 公式	Explanation / 解释
Real Distance = Map Distance × Denominator of Scale	If scale is 1 : D, then 1 cm on map = D cm real. / 比例尺为 1 : D，则图上 1 厘米 = 实地 D 厘米。
Real distance (km) = Map distance (cm) × D ÷ 100,000	Quick conversion to kilometres. / 快速换算为公里。

Example: On a 1:50,000 map, two points are 7.5 cm apart. Real distance = 7.5 × 50,000 = 375,000 cm = 3.75 km.

示例：在 1:50,000 地图上，两点相距 7.5 厘米。实地距离 = 7.5 × 50,000 = 375,000 厘米 = 3.75 公里。

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2. Gradient and Contour Lines | 坡度与等高线

Gradient measures how steep a slope is. It is calculated as the vertical rise over the horizontal run. On an Ordnance Survey map, you find the difference in height between two contour lines, and the horizontal distance between them along the ground.

坡度用来衡量斜坡的陡缓程度，计算公式为垂直上升高度除以水平距离。在英国地形测量图上，你需要找到两条等高线之间的高差，以及它们之间的水平地面距离。

The standard formula: Gradient = Vertical Height Difference (m) ÷ Horizontal Distance (m), often expressed as a ratio 1 : R. To obtain R, divide horizontal distance by vertical rise.

标准公式：坡度 = 垂直高差（米）÷ 水平距离（米），通常表示为比值 1 : R。R 等于水平距离除以垂直上升高度。

Gradient = 1 : (Horizontal distance ÷ Vertical rise)

Example: Height difference = 20 m; horizontal distance = 500 m. Gradient = 20 / 500 = 1 / 25, i.e. 1:25.

示例：高差 = 20 米；水平距离 = 500 米。坡度 = 20 / 500 = 1 / 25，即 1 : 25。

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3. River Discharge | 河流流量

Discharge is the volume of water flowing through a river channel at a given point, measured in cubic metres per second (cumecs). It helps geographers understand river regimes, flood risk, and seasonal variations.

流量指在某一断面上单位时间内流过河槽的水的体积，单位是立方米/秒。它帮助地理学者理解河流的年内变化、洪水风险和季节变化。

The fundamental formula: Discharge (Q) = Cross-sectional Area (A) × Average Velocity (V). Area is measured in m² by multiplying channel width by average depth. Velocity is measured in m/s.

基本公式：流量 (Q) = 过水断面面积 (A) × 平均流速 (V)。面积以平方米表示，通过河宽乘以平均水深求得；流速单位是米/秒。

Q = A × V

If a river is 8 m wide and average depth is 1.5 m, A = 12 m². If velocity is 2 m/s, Q = 12 × 2 = 24 m³/s.

如果一条河宽 8 米，平均水深 1.5 米，则 A = 12 平方米；若流速为 2 米/秒，则流量 Q = 12 × 2 = 24 立方米/秒。

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4. Population Density | 人口密度

Population density tells us how crowded an area is. It is the average number of people per unit of land area, often per square kilometre (km²). High density areas are typically urban settlements; low density areas are often rural or harsh environments.

人口密度表示一个地区的拥挤程度，即平均每单位面积土地上的人口数，通常用每平方公里人口数表示。高密度区通常是城市居民点，低密度区常为乡村或恶劣环境。

Population Density = Total Population ÷ Total Land Area (km²)

Example: A city has 250,000 people living in an area of 125 km². Density = 250,000 ÷ 125 = 2,000 people per km².

示例：某城市有 25 万人，面积 125 平方公里。密度 = 250,000 ÷ 125 = 每平方公里 2,000 人。

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

Birth rate (BR) and death rate (DR) are expressed as the number of live births or deaths per 1,000 people per year. The difference between them gives the natural increase (or decrease) without migration. These are vital signs for understanding population change and the Demographic Transition Model.

出生率与死亡率以每年每千人中活产婴儿数或死亡人数表示。两者的差值得出自然增长（或减少），不包括迁移。这是理解人口变化和人口转变模型的关键指标。

BR (‰) = (Number of live births ÷ Total population) × 1,000

DR (‰) = (Number of deaths ÷ Total population) × 1,000

Natural Increase (‰) = BR – DR

Often, to get the Natural Increase Rate as a percentage, divide by 10: e.g., BR 25‰, DR 10‰ → Natural increase 15‰ → 1.5%.

经常将自然增长率转换为百分比，需除以 10：例如，出生率 25‰，死亡率 10‰ → 自然增长 15‰ → 1.5%。

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6. Migration Rate | 迁移率

Migration is the movement of people across a defined boundary, involving a change of residence. Net migration is the difference between in-migrants (immigrants) and out-migrants (emigrants). A positive net migration means more people arriving; negative means more leaving.

迁移是人口跨越特定边界并改变居住地的流动。净迁移等于迁入人口减迁出人口。净迁移为正意味着迁入多于迁出，为负则相反。

Net Migration = Immigration – Emigration

Net Migration Rate (‰) = (Net Migration ÷ Total Population) × 1,000

Example: In a year, a town receives 1,200 in-migrants and loses 800 out-migrants. Total population = 40,000. Net migration = 400; rate = (400 ÷ 40,000) × 1,000 = 10‰.

示例：一年内某镇接收 1,200 人迁入，800 人迁出，总人口 4 万。净迁移 = 400；净迁移率 = (400 ÷ 40,000) × 1,000 = 10‰。

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7. Population Growth Rate | 人口增长率

The total population growth rate combines natural increase and net migration to show the overall annual change in population. It is usually given as a percentage. A country growing at 2% per year will double its population in about 35 years (Rule of 70: 70 ÷ 2 = 35).

总人口增长率结合了自然增长与净迁移，显示人口的年度总体变化，通常以百分比表示。一个国家每年增长 2%，大约 35 年人口翻一番（70 法则：70 ÷ 2 = 35）。

Growth Rate (%) = [(Natural Increase + Net Migration) ÷ Total Population] × 100

Or using per thousand rates: Growth Rate (%) = (Natural Increase Rate (‰) + Net Migration Rate (‰)) ÷ 10.

或利用千分率：增长率 (%) = (自然增长率(‰) + 净迁移率(‰)) ÷ 10。

Example: Natural increase 12‰, net migration rate -3‰ → combined = 9‰ → 0.9% growth.

示例：自然增长率 12‰，净迁移率 -3‰ → 合计 9‰ → 0.9% 增长率。

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8. Percentage Change | 百分比变化

Percentage change is a universal method to compare differences over time or between places. It answers: ‘By what percentage has the value increased or decreased?’ Always use the original (starting) value as the denominator.

百分比变化是一种通用的比较方法，用于比较随时间推移或地区间的差异。它回答：“数值增加或减少了百分之几？” 始终以原始（起始）值作分母。

% Change = [(New Value – Original Value) ÷ Original Value] × 100

If the result is positive, it’s an increase; if negative, it’s a decrease. Use this for tourism numbers, rainfall totals, or population figures.

结果为正值表示增加；负值表示减少。可用于旅游人数、降雨总量或人口数据等。

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9. Temperature Range and Mean | 气温较差与平均气温

Climate data analysis often needs the temperature range (the difference between the highest and lowest temperatures) and the mean annual temperature. These help classify climates (e.g., maritime vs continental) and support climate graph interpretation.

气候数据分析常需要气温较差（最高与最低气温之差）和年平均气温。这些有助于区分气候类型（如海洋性气候与大陆性气候），并支持气候图表解读。

Temperature Range = Maximum Temperature – Minimum Temperature

Mean Annual Temperature = Sum of 12 monthly means ÷ 12

In a climate graph, look for the highest and lowest points on the temperature curve. A large range usually suggests inland locations far from the sea.

在气候图上，找出气温曲线上的最高点和最低点。较大的年较差通常代表远离海洋的内陆地区。

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10. Measuring Area on Maps | 地图上面积测量

Estimating the area of a feature (a lake, woodland, or farm) on a map requires converting the area measured on the map to the real-world area, using the map scale squared. The key is to remember that scale applies to linear measures, so the area conversion factor is scale².

估算地图上某一要素（如湖泊、林地或农场）的面积，需要借助比例尺的平方将图上面积转换为实地面积。关键是记住：比例尺适用于线性量度，面积换算系数为比例尺的平方。

Real Area = Map Area × (Scale Factor)²

On a 1:50,000 map, 1 cm² on the map = 50,000 cm × 50,000 cm = 2,500,000,000 cm² = 0.25 km². Count squares on a grid overlay to estimate map area first.

在 1:50,000 地图上，图上 1 平方厘米 = 50,000 厘米 × 50,000 厘米 = 25 亿平方厘米 = 0.25 平方公里。先用方格纸覆盖地图并数格子估算图上面积。

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11. Cross-Section Drawing and Vertical Exaggeration | 剖面图与垂直夸大

A cross-section shows the shape of the land along a line between two points. Vertical exaggeration (VE) is used to make gentle slopes more visible. VE compares the vertical scale to the horizontal scale. If VE = 5, the vertical dimension is 5 times larger than reality relative to the horizontal.

剖面图展示了两点之间地表的起伏形态。垂直夸大（VE）用于使平缓的坡度更加明显。VE 比较垂直比例尺与水平比例尺，如果 VE = 5，则垂直方向被放大了 5 倍（相对水平方向）。

VE = Vertical Scale (as a fraction) ÷ Horizontal Scale (as a fraction)

Both scales must be expressed as representative fractions (e.g., 1 cm to 50 m = 1:5,000).

两种比例尺都必须化作比例式（如 1 厘米代表 50 米 = 1:5,000）。

Example: Horizontal scale 1:50,000; vertical scale 1 cm to 500 m (1:50,000). VE = 1/50,000 ÷ 1/50,000 = 1. If vertical scale were 1:10,000, VE = (1/10,000) ÷ (1/50,000) = 5.

示例：水平比例尺 1:50,000；垂直比例尺 1 厘米代表 500 米 (1:50,000)，VE = (1/50,000) ÷ (1/50,000) = 1。若垂直比例尺为 1:10,000，则 VE = 5。

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12. GDP per Capita | 人均 GDP

Gross Domestic Product (GDP) per capita is used as an indicator of economic development. It is the total value of goods and services produced in a country in a year divided by the mid-year population. Higher GDP per capita generally suggests a higher standard of living.

人均国内生产总值（人均 GDP）用作经济发展的指标。它是一国一年内生产的商品和服务总价值除以年中人口数。人均 GDP 越高，通常表明生活水平越高。

GDP per capita = Total GDP ÷ Population

Example: A country’s GDP = $500 billion, population = 50 million. GDP per capita = 500,000,000,000 ÷ 50,000,000 = $10,000.

示例：某国 GDP = 5,000 亿美元，人口 5,000 万。人均 GDP = 500,000,000,000 ÷ 50,000,000 = 10,000 美元。

Note also the Human Development Index (HDI), which combines life expectancy, education, and income into a single score between 0 and 1. While not a single formula, it is often treated as a ‘theorem’ of development measurement.

还应注意人类发展指数 (HDI)，它将预期寿命、教育水平和收入综合成一个 0 到 1 之间的分数。虽非单一公式，但常被视为衡量发展的“定理”。

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