📚 KS3 AQA Geography: Formulas and Theorems Quick Reference Handbook | KS3 AQA 地理：公式定理速查手册
This handbook provides a concise collection of essential formulas, rules, and key calculations you need for KS3 AQA Geography. Use it to quickly revise map skills, population measures, climate data, river characteristics and economic indicators.
本手册提供了 KS3 AQA 地理所需的基本公式、定理和关键计算的简明集合。用于快速复习地图技能、人口测量、气候数据、河流特征和经济指标。
1. Map Scale and Distance Calculations | 地图比例尺与距离计算
Actual Distance = Map Distance × Scale Denominator
On a 1:50,000 map, if a line measures 4 cm, the ground distance is 4 cm × 50,000 = 200,000 cm = 2 km.
在一幅 1:50,000 地图上，如果一条线长为 4 厘米，则地面距离为 4 cm × 50,000 = 200,000 cm = 2 km。
To convert centimetres to kilometres, divide by 100,000 (since 1 km = 100,000 cm). For metres, divide by 100.
要将厘米转换成千米，除以 100,000（因为 1 km = 100,000 cm）。转换成米则除以 100。
To calculate area from a map, measure length and width in cm, convert each to ground distance, and multiply. The result must be expressed in square units (m² or km²).
计算地图上的面积时，用厘米测量长和宽，分别转换为地面距离后相乘。结果需以平方单位（m² 或 km²）表示。
2. Measuring Slope Gradient | 测量坡度梯度
Gradient (%) = (Vertical Rise ÷ Horizontal Run) × 100
A slope with a vertical rise of 20 m over a horizontal distance of 100 m has a gradient of (20/100)×100 = 20%.
垂直升高 20 米、水平距离 100 米的斜坡，其坡度为 (20/100)×100 = 20%。
Always ensure both measurements use the same unit. Contour lines on a map help determine vertical rise; closely spaced contours indicate a steep gradient.
始终确保上升和水平距离使用相同单位。地图上的等高线有助于确定垂直升高；等高线密集表示陡坡。
3. Grid References and Compass Directions | 网格参考与罗盘方向
A four-figure grid reference (e.g., 1532) locates a 1 km × 1 km square. Read eastings first (15) then northings (32) — “along the corridor and up the stairs”.
四位数网格参考（如 1532）定位一个 1 km × 1 km 的方格。先读东向坐标 (15)，再读北向坐标 (32)——“先走走廊，再上楼梯”。
A six-figure grid reference (e.g., 155325) pinpoints a 100 m × 100 m square. Divide each easting and northing into tenths and add the extra digit.
六位数网格参考（如 155325）精确定位 100 m × 100 m 的方格。将每一条东向和北向坐标细分为十分位，再加上额外数字。
The eight compass directions are N, NE, E, SE, S, SW, W, NW. Bearings measure direction as a three‑digit angle clockwise from North (000° to 360°).
八个罗盘方向为 N、NE、E、SE、S、SW、W、NW。方位角是从正北顺时针测量的三位数角度（000° 至 360°）。
4. Demographic Formulas: Birth Rate, Death Rate, Natural Increase | 人口统计公式：出生率、死亡率、自然增长率
Birth Rate = (Number of live births in a year / Total population) × 1,000
The crude birth rate shows the number of live births per 1,000 people per year.
粗出生率表示每年每 1,000 人中的活产儿数量。
Death Rate = (Number of deaths in a year / Total population) × 1,000
Similarly, the crude death rate is expressed per 1,000 people per year. It reflects the general health conditions of a population.
同样，粗死亡率以每年每 1,000 人表示，反映了人口的整体健康状况。
Natural Increase = Birth Rate – Death Rate
Natural increase can be positive (growing population) or negative (declining population). It does not account for migration.
自然增长率可为正（人口增长）或负（人口减少）。它不包含迁移因素。
To express natural increase as a percentage, divide the per‑1,000 value by 10: (Natural increase per 1,000) / 10 = %.
要将自然增长率表示为百分比，将每千人值除以 10：(每千人自然增长) / 10 = %。
5. Population Density | 人口密度
Population Density = Total Population / Total Land Area (people per km²)
For example, if a country has 60 million people and an area of 500,000 km², density = 60,000,000 / 500,000 = 120 people/km².
例如，某国人口 6000 万，面积 50 万 km²，则人口密度 = 60,000,000 / 500,000 = 120 人/km²。
Population density helps explain patterns such as sparse settlement in mountains or dense cities along coasts. Always check the units of area.
人口密度有助于解释山区人口稀少或沿海城市密集等分布格局。务必检查面积单位。
6. Urbanisation Rate | 城市化率
Urbanisation Rate (%) = (Urban population / Total population) × 100
This measures the proportion of people living in urban areas. An increase over time indicates urbanisation, often linked to industrialisation.
它衡量居住在城市地区的人口比例。随时间推移而增加表示城市化，通常与工业化相关。
Comparing rates between countries requires careful interpretation; a high rate of urbanisation in a developing country can mean rapid rural‑to‑urban migration.
比较不同国家的城市化率需谨慎；发展中国家的高城市化率可能意味着快速的乡城迁移。
7. Climate Data Calculations | 气候数据计算
Mean Daily Temperature = (Maximum temperature + Minimum temperature) / 2
For a month, average all the daily means to get the monthly mean temperature. This is used when constructing climate graphs.
对于一个月，计算所有日平均值的平均数得到月平均温度。这在绘制气候图时使用。
Temperature Range = Highest temperature – Lowest temperature
The diurnal (daily) range is the difference between day and night temperatures; the annual range uses monthly means. Large annual ranges often indicate a continental climate.
日较差是白天与夜间气温之差；年较差使用月平均气温。年较差大通常表明大陆性气候。
Total Annual Rainfall = Sum of all monthly rainfall measurements (mm)
Always check if the data is in millimetres or centimetres. 1 mm of rainfall equals 1 litre of water per square metre.
务必检查数据单位是毫米还是厘米。1 mm 降雨量相当于每平方米 1 升水。
8. River Discharge and Velocity | 河流流量与流速
Discharge (Q) = Cross-sectional area (A) × Velocity (V)
Discharge is the volume of water flowing past a point every second, expressed in cubic metres per second (cumecs). A larger, faster river has higher discharge.
流量是每秒流过某点的水体积，单位为立方米/秒（cumecs）。河道越大、水流越快，流量越高。
Cross-sectional area (A) = Channel width × Average depth
Measure the water surface width (m) and take several depth readings across the channel, then calculate the mean depth. Multiply width by average depth.
测量水面宽度（米），并在河道中多点测量水深，计算平均深度。然后将宽度乘以平均深度。
Velocity can be estimated using a float and a stopwatch: velocity (m/s) = distance travelled (m) / time (s). In the field, a flowmeter gives more accurate readings.
流速可用浮标和秒表估算：流速 (m/s) = 流动距离 (m) / 时间 (s)。野外使用流速计测量更精确。
9. Economic Indicators: GDP and GDP per Capita | 经济指标：国内生产总值与人均 GDP
GDP per capita = Total GDP / Total population
This gives the average economic output per person and is often used to compare living standards between countries. Note that it does not reflect income distribution.
它表示人均经济产出，常用于比较各国生活水平。注意它不反映收入分配状况。
GDP Growth Rate (%) = [(GDP in current year – GDP in previous year) / GDP in previous year] × 100
A positive growth rate indicates economic expansion; a negative value signals contraction. Used to track economic development over time.
正增长率表明经济扩张；负值表示收缩。用于追踪经济发展的变化。
10. Percentage Change in Land Use | 土地利用变化百分比
Percentage Change = ((New Value – Old Value) / Old Value) × 100
This formula is essential for analysing deforestation, urban sprawl, agricultural expansion, or other land‑cover changes over time.
该公式对分析森林砍伐、城市扩张、农业扩张或其他土地覆盖变化随时间的变化至关重要。
A negative result indicates a decrease (e.g., loss of forest of 50 km² from an original 200 km² gives -25%). Remember to include the appropriate unit, such as % or hectares.
负值表示减少（例如，森林从原有的 200 km² 减少 50 km²，变化百分比为 -25%）。记得标注适当的单位，如 % 或公顷。
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