📚 Year 8 OCR Geography: Quick-Reference Formula & Theorem Handbook | Year 8 OCR 地理：公式定理速查手册
This handbook gathers the essential formulas, theorems, and quick calculation methods you will encounter in the Year 8 OCR Geography course. Use it to revise key concepts such as population dynamics, map skills, climate data, and development indicators. Each entry is presented with a clear formula, an example, and its real-world application.
本手册汇集了 Year 8 OCR 地理课程中的重要公式、定理和速算方法。你可以用它来复习人口动态、地图技能、气候数据和发展指标等核心概念。每个条目都配有清晰的公式、示例和实际应用说明。
1. Population Density | 人口密度
Population density measures how crowded an area is. The formula divides the total population by the land area. It is usually expressed in people per square kilometre (people/km²).
人口密度衡量一个地区的拥挤程度。公式是用总人口除以土地面积。单位通常是每平方公里人数（人/平方公里）。
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 city has 500,000 people and covers 250 km², the population density is 500,000 ÷ 250 = 2,000 people/km². Sparsely populated areas like deserts have low density, while urban centres have high density. Population maps often use this value to compare regions.
例如，如果一个城市有 50 万人，面积为 250 平方公里，人口密度就是 500,000 ÷ 250 = 2,000 人/平方公里。人口稀少的地区如沙漠密度低，而城市中心密度高。人口分布图常用这个数值来比较不同地区。
2. Natural Increase Rate | 自然增长率
Natural increase shows how a population grows without considering migration. It is the difference between the crude birth rate and the crude death rate, usually given per 1,000 people per year.
自然增长率显示在不考虑迁移的情况下人口如何增长。它是粗出生率与粗死亡率之间的差值，通常以每年每千人表示。
Natural Increase Rate (‰) = Birth Rate (‰) – Death Rate (‰)
自然增长率（‰） = 出生率（‰） – 死亡率（‰）
Suppose birth rate is 22 per 1,000 and death rate is 8 per 1,000. The natural increase is 22 – 8 = 14 per 1,000, meaning the population grows by 1.4% per year. A negative result indicates a declining population, as seen in some developed countries.
假设出生率为每千人 22，死亡率为每千人 8。自然增长为 22 – 8 = 14 每千人，意味着人口每年增长 1.4%。负值表示人口在减少，这在一些发达国家会出现。
3. Net Migration Rate | 净迁移率
Net migration rate accounts for people moving in (immigration) and out (emigration) of a region. It also uses rates per 1,000 people to allow comparisons between different-sized populations.
净迁移率计算的是一个地区迁入（移民）和迁出（外移）的人口差额。同样以每千人比率表示，便于不同人口规模的地区进行比较。
Net Migration Rate (‰) = Immigration Rate (‰) – Emigration Rate (‰)
净迁移率（‰） = 迁入率（‰） – 迁出率（‰）
A positive net migration rate means more people are arriving than leaving, often boosting urban populations. Negative values highlight regions losing workforce, such as some rural areas. Combining natural increase and net migration gives total population change.
正的净迁移率意味着迁入人口多于迁出人口，通常会推动城市人口增长。负值则表明地区在流失劳动力，比如一些农村地区。自然增长加上净迁移就是总人口变化。
4. Total Population Change | 总人口变化
Total population change combines both natural growth and net migration. It helps geographers understand whether a place’s population is rising or falling overall.
总人口变化结合了自然增长和净迁移。它帮助地理学者了解一个地区的总人口是在增加还是减少。
Total Population Change = (Births – Deaths) + (Immigrants – Emigrants)
总人口变化 = （出生人数 – 死亡人数） + （迁入人数 – 迁出人数）
For a country with 12,000 births, 7,000 deaths, 3,000 immigrants and 2,000 emigrants, the change is (12,000 – 7,000) + (3,000 – 2,000) = 5,000 + 1,000 = 6,000 people. This total can be expressed as an absolute number or as a percentage change.
对一个有 12,000 出生、7,000 死亡、3,000 迁入和 2,000 迁出的国家来说，变化为 (12,000 – 7,000) + (3,000 – 2,000) = 5,000 + 1,000 = 6,000 人。这个总数可以用绝对数字或百分比变化来表示。
5. Dependency Ratio | 抚养比
The dependency ratio compares the economically dependent part of the population (young under 15 and elderly over 64) with the working-age population (15–64). The result is multiplied by 100 to give a percentage-like figure.
抚养比将经济上依赖他人的群体（15 岁以下少儿和 64 岁以上老人）与劳动年龄人口（15–64 岁）进行比较。计算结果乘以 100，得到一个类似百分比的数值。
Dependency Ratio (%) = [(Population 0–14 + Population 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
A high dependency ratio, such as 65%, means there are many dependents for every 100 working-age people. This puts pressure on healthcare and education. Countries with ageing populations often see rising dependency ratios.
高抚养比，比如 65%，意味着每 100 名劳动年龄人口要抚养很多非劳动人口，这会给医疗和教育带来压力。老龄化国家通常抚养比会不断上升。
6. Crude Birth and Death Rates per 1,000 | 粗出生率和粗死亡率
Crude rates are fundamental in population geography. They are calculated per 1,000 people per year to standardise comparisons between countries of different sizes.
粗率是人口地理中的基础指标。它们按每年每千人计算，以标准化不同规模国家之间的比较。
Crude Birth Rate (CBR) = (Total Births ÷ Total Population) × 1,000
粗出生率 (CBR) = （总出生人数 ÷ 总人口） × 1,000
Crude Death Rate (CDR) = (Total Deaths ÷ Total Population) × 1,000
粗死亡率 (CDR) = （总死亡人数 ÷ 总人口） × 1,000
A CBR of 30‰ is typical of many developing nations, while a CDR below 10‰ often reflects better healthcare. These values feed directly into the natural increase formula. Remember: the ‰ symbol means ‘per thousand’.
30‰ 的粗出生率在许多发展中国家比较常见，而低于 10‰ 的粗死亡率往往反映了更好的医疗条件。这些数值直接用于自然增长率公式。请记住：‰ 符号表示“每千”。
7. Population Doubling Time – Rule of 70 | 人口翻倍时间——70 法则
To estimate how long it takes for a population to double at a constant growth rate, geographers apply the Rule of 70. This is a quick approximation widely used in demography.
要估算人口在恒定增长率下翻倍所需的时间，地理学者会运用 70 法则。这是人口学中广泛使用的快速近似方法。
Doubling Time (years) ≈ 70 ÷ Annual Growth Rate (%)
翻倍时间（年） ≈ 70 ÷ 年增长率 (%)
If a country’s annual growth rate is 2%, doubling time ≈ 70 ÷ 2 = 35 years. If growth slows to 1%, it takes about 70 years. The lower the growth rate, the longer the doubling time. This helps planners forecast future resource needs.
如果一个国家的年增长率为 2%，翻倍时间约等于 70 ÷ 2 = 35 年。如果增长率降至 1%，就需要约 70 年。增长率越低，翻倍时间越长。这有助于规划者预测未来的资源需求。
8. Climate Graphs: Temperature Range and Total Precipitation | 气候图表：气温年较差和总降水量
Climate graphs (climographs) combine monthly temperature and rainfall data. Two key calculations help interpret them: the annual temperature range and the total annual precipitation.
气候图表（气候图解）结合了月均温和月降水量数据。两个关键计算有助于解读它们：气温年较差和年总降水量。
Temperature Range = Highest Monthly Temperature – Lowest Monthly Temperature
气温年较差 = 最高月平均温度 – 最低月平均温度
Total Annual Precipitation = Sum of all 12 monthly precipitation values
年总降水量 = 所有 12 个月降水量数值之和
A large temperature range, like 25°C, suggests a continental climate far from the sea. A small range, such as 3°C, points to maritime or equatorial influences. Total annual rainfall distinguishes wet tropical climates (over 2,000 mm) from arid deserts (below 250 mm).
较大的气温年较差，如 25°C，表明是远离海洋的大陆性气候。较小的年较差，如 3°C，则指向海洋性或赤道气候影响。年总降水量可以区分湿润的热带气候（超过 2,000 毫米）和干旱沙漠（低于 250 毫米）。
9. Gradient (Slope) on Maps | 地图上的坡度（斜率）
Gradient measures the steepness of a slope using contour lines on topographic maps. It is expressed as a ratio, fraction, or percentage.
坡度利用地形图上的等高线来测量斜坡的陡峭程度。它用比率、分数或百分比来表示。
Gradient = Vertical Interval (Rise) ÷ Horizontal Equivalent (Run)
坡度 = 垂直高差（升高） ÷ 水平距离（平距）
If the contour interval is 20 metres and the horizontal distance between two contours on the map is 200 metres (using the scale to convert), the gradient is 20 ÷ 200 = 1/10 or 1:10. A 1:5 slope is steeper than 1:20. The smaller the denominator, the steeper the terrain.
如果等高线间距为 20 米，地图上两条等高线之间的水平距离为 200 米（利用比例尺换算），那么坡度就是 20 ÷ 200 = 1/10 或 1:10。1:5 的坡度比 1:20 更陡。分母越小，地形越陡。
10. Map Scale Conversions | 地图比例尺换算
Scale links map distance to real-world distance. You must be able to convert between a representative fraction (RF), a verbal statement, and a linear scale bar.
比例尺将地图距离与实地距离联系起来。你必须能够在数字比例尺（分数式）、文字说明和直线比例尺之间进行转换。
Real Distance = Map Distance × Scale Factor
实地距离 = 地图距离 × 比例尺因子
For a 1:50,000 scale, 1 cm on the map represents 50,000 cm in reality, which is 500 metres or 0.5 km. So, 4 cm on the map equals 4 × 0.5 = 2 km in the real world. Always convert units carefully: 100,000 cm = 1 km.
对于 1:50,000 的比例尺，地图上的 1 厘米代表实地 50,000 厘米，即 500 米或 0.5 公里。因此，地图上 4 厘米等于 4 × 0.5 = 2 公里的实地距离。务必小心转换单位：100,000 厘米 = 1 公里。
11. GDP per Capita | 人均国内生产总值
Gross Domestic Product (GDP) per capita is a common development indicator. It divides the total value of goods and services produced in a country by its population.
人均国内生产总值（GDP）是一个常见的发展指标。它用一国生产的商品和服务的总价值除以该国人口。
GDP per Capita = Total GDP ÷ Total Population
人均 GDP = GDP 总量 ÷ 总人口
While GDP per capita gives an average income level, it has limitations: it does not show inequality or non-monetary aspects of well-being. Geographers also use the Human Development Index (HDI), which combines income, life expectancy, and education years.
虽然人均 GDP 显示了平均收入水平，但它有局限性：无法反映不平等现象或非金钱方面的福祉。地理学者也会使用人类发展指数（HDI），该指数综合了收入、预期寿命和受教育年限。
12. Water Balance and River Discharge | 水量平衡与河流流量
Understanding river basins requires knowledge of water balance. The simple equation links precipitation, evapotranspiration, runoff, and changes in soil storage.
理解河流流域需要掌握水量平衡知识。简单的方程将降水、蒸散发、径流和土壤储水变化联系起来。
Runoff (Q) = Precipitation (P) – Evapotranspiration (E) ± Change in Storage (ΔS)
径流 (Q) = 降水量 (P) – 蒸散发 (E) ± 储水量变化 (ΔS)
River discharge, the volume of water flowing past a point per second, is calculated as cross-sectional area × average velocity. While this appears more in physical geography, Year 8 students often meet the idea when studying flooding and water management.
河流流量，即每秒通过某点的水体积，计算方法为横截面积 × 平均流速。虽然这在自然地理中更为常见，但 Year 8 学生在学习洪水和水利管理时经常会接触到这个概念。
Discharge (m³/s) = Channel Cross-sectional Area (m²) × Velocity (m/s)
流量 (m³/s) = 河道横截面积 (m²) × 流速 (m/s)
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