📚 Year 8 SQA Geography: Quick-Reference Handbook of Formulas & Theorems | 八年级SQA地理：公式定理速查手册
Geography is full of measurable patterns and numerical relationships that help us understand the world. This quick-reference handbook brings together the essential formulas and key ideas you will use in Year 8 SQA Geography, from map-reading calculations to population statistics and climate data. Keep it handy for homework, revision, and fieldwork – knowing the right formula makes data meaningful and mapping accurate.
地理学充满了可测量的模式和数量关系，这些关系帮助我们理解世界。这本速查手册汇集了你在八年级SQA地理课程中将会用到的基本公式和关键概念，从地图判读计算到人口统计和气候数据。无论是做作业、复习还是野外考察，把它放在手边——掌握正确的公式能让数据变得有意义，也让地图判读更加精确。
1. Map Scales and Distance Calculations | 比例尺与距离计算
A map scale shows the ratio between a distance on the map and the actual distance on the ground. For example, a scale of 1:25,000 means that 1 cm on the map represents 25,000 cm (250 m) in reality. To find the real-world straight-line distance, you measure the map distance in centimetres and multiply by the scale denominator.
地图比例尺表示图上距离与实际地面距离的比。例如，1:25,000的比例尺意味着图上1厘米代表实际25,000厘米（250米）。要计算实地的直线距离，你需要量出地图上的厘米数，再乘以比例尺分母。
AD = MD × SD
实际距离 = 地图距离 × 比例尺分母
where AD = actual ground distance (cm), MD = distance measured on the map (cm), and SD = scale denominator (e.g. 25,000). After obtaining AD in centimetres, you convert to metres or kilometres by dividing by 100 or 100,000.
其中 AD 代表实际地面距离（厘米），MD 代表在图上量出的距离（厘米），SD 代表比例尺分母（例如25,000）。算出以厘米为单位的 AD 后，再除以 100 或 100,000，即可换算为米或千米。
To measure a winding route such as a river or road, use a piece of string, follow the curves, then straighten the string and measure its length against the map scale bar or apply the formula.
如果要量测弯曲的路线，比如一条河流或道路，可以用一根棉线沿曲线摆放，然后将线拉直，用直尺量出其长度，再按照比例尺换算或将棉线与比例尺线段对比即可。
2. Estimating Area on Maps | 地图面积估算
To estimate the area of a feature such as a forest, lake or urban zone, you can use the grid-square method or the proportional formula. Count the number of complete grid squares covered by the feature and add fractions for partial squares. Then multiply by the area represented by one square on the ground.
要估算一片森林、湖泊或城区这类地物的面积，可以使用方格法或比例面积公式。数出地物覆盖的完整方格数目，不足一格的按比例估算后加上去，再乘以每个方格所代表的实际面积。
Actual Area = Map Area × (SD)²
实际面积 = 图上面积 × (比例尺分母)²
If you measure the map area in square centimetres, the actual area initially comes out in square centimetres. You then convert to square metres (divide by 10,000) or square kilometres (divide by 10,000,000,000). The scale factor is squared because area is two-dimensional.
如果你以平方厘米量算图上面积，实际面积的初始单位也是平方厘米。接着换算成平方米（除以10,000）或平方千米（除以10,000,000,000）。比例尺分母需要平方，因为面积是二维量。
3. Slope Gradient | 坡度计算
Slope gradient tells you how steep the land is. It is usually expressed as a ratio, a percentage, or an angle in degrees. On a map, you determine the vertical rise (difference in height between two points) and the horizontal run (the ground distance between them).
坡度表示地表的陡峭程度，通常用比、百分比或角度（度）来表示。在地图上，你需要确定两点之间的垂直升降（高差）与水平距离（实地距离）。
Gradient (%) = (Vertical Rise ÷ Horizontal Run) × 100
坡度(%) = (垂直高差 ÷ 水平距离) × 100
For a slope angle, use the inverse tangent: θ = tan⁻¹ (rise / run). A gradient of 10% means the land rises 10 metres for every 100 metres of horizontal distance. When reading contour maps, remember that closely spaced contours indicate a steep slope, while widely spaced ones show a gentle slope.
若要求坡度角，可用反正切函数：θ = tan⁻¹ (高差 / 水平距离)。10%的坡度表示每水平前进100米，地面上升10米。在判读等高线地图时，记住等高线密集表示陡坡，稀疏表示缓坡。
4. Contours and Vertical Interval | 等高线与垂直间隔
Contours are lines on a map joining points of equal elevation. The vertical interval (VI), also called contour interval, is the height difference between two successive contour lines. This value is always stated in the map legend. You can use it to calculate the height of a point lying between two contours by interpolation.
等高线是地图上连接相同高度点的线条。垂直间隔（VI），也称等高距，是相邻两条等高线之间的高差。这个数值总会标注在图例中。你可以利用它，通过内插法估算两条等高线之间某点的高度。
The total relief of an area is the difference between the highest and lowest points: Relief = Max Elevation − Min Elevation. Both values are obtained from spot heights or by counting contours.
一个地区的总起伏是最高点与最低点之间的差值：起伏 = 最高海拔 − 最低海拔。两个数值都可以从高程点注记或通过数等高线获得。
5. Population Density | 人口密度
Population density measures how crowded an area is. It shows the average number of people living in a square kilometre of land. This formula is a cornerstone of human geography because it helps explain land use, service provision, and settlement patterns.
人口密度衡量一个地区的拥挤程度，表示每平方千米土地上平均居住的人数。这是人文地理学的一个核心公式，有助于解释土地利用、服务提供和聚落形态。
PD = P ÷ A
人口密度 = 总人口 ÷ 总面积
where P = total population and A = total land area in square kilometres (or square miles). A high population density often means an urban or densely farmed area, while a low density suggests rural or harsh environments.
其中 P 代表总人口，A 代表以平方千米（或平方英里）为单位的总面积。人口密度高通常意味着城市或集约农业区，而密度低则可能指示乡村或恶劣环境。
6. Birth Rate and Death Rate | 出生率与死亡率
Crude Birth Rate (CBR) and Crude Death Rate (CDR) are expressed per 1,000 people per year. They allow fair comparison between countries of different sizes. The formula uses the total number of live births or deaths in one year and the mid-year population.
粗出生率（CBR）和粗死亡率（CDR）以每年每千人为单位表示，便于在不同国家之间进行公平比较。该公式使用一年内的活产总数或死亡总数以及年中人口数。
BR = (B ÷ P) × 1000
出生率 = (出生人数 ÷ 总人口) × 1000
DR = (D ÷ P) × 1000
死亡率 = (死亡人数 ÷ 总人口) × 1000
A high birth rate and high death rate often indicate a less economically developed country, while low birth and low death rates are typical of more developed nations. These rates are key components of the Demographic Transition Model.
高出生率和高死亡率往往出现在经济欠发达国家，而低出生率和低死亡率则是较发达国家的典型特征。这些比率是人口转变模型的关键组成部分。
7. Natural Increase and Net Migration | 自然增长率与净迁移
Natural increase (NI) is the difference between the birth rate and the death rate. It does not include migration. It is expressed as a percentage or per thousand. When natural increase is positive, the population grows from births alone.
自然增长（NI）指出生率与死亡率之差，不包含人口迁移。它用百分比或千分比表示。当自然增长为正时，仅靠出生人口就会使总人口增加。
NI = BR − DR
自然增长率 = 出生率 − 死亡率
Net migration rate accounts for the difference between immigration (inward movement) and emigration (outward movement) per 1,000 people. A positive net migration means more people moving in than out.
净迁移率反映的是每千人中迁入与迁出的人数之差。净迁移为正表示迁入人数多于迁出人数。
NM = (I − E) ÷ P × 1000
净迁移率 = (迁入人数 − 迁出人数) ÷ 总人口 × 1000
8. Population Growth Rate | 人口增长率
The overall population growth rate combines natural increase and net migration. It tells you the actual rate at which a country’s population is changing each year. This metric is vital for planning housing, schools, and healthcare.
总人口增长率综合了自然增长和净迁移的影响，它告诉你一个国家每年人口的实际变化速度。这个指标对住房、学校和医疗规划至关重要。
GR = NI + NM
人口增长率 = 自然增长率 + 净迁移率
Both components are usually expressed per thousand or as a percentage. For example, if NI = 5 per thousand and NM = 2 per thousand, the growth rate is 7 per thousand, or 0.7%. Even a small percentage can lead to large absolute increases in populous countries.
两个组成部分通常都以千分比或百分比表示。例如，如果自然增长率为千分之五，净迁移率为千分之二，那么增长率为千分之七，即0.7%。在人口众多的国家，即使百分比很小，绝对增加量也可能很大。
9. Urbanisation Level | 城市化水平
Urbanisation measures the proportion of a population living in towns and cities compared to rural areas. The formula is simple but powerful for tracking how regions evolve from agricultural to industrial and service-based economies.
城市化衡量人口中居住在城镇的比例，与乡村地区相对照。这个公式虽然简单，但对于跟踪一个地区从农业经济向工业和服务型经济转型的过程十分有用。
U% = (Urban Population ÷ Total Population) × 100
城市化率 = (城镇人口 ÷ 总人口) × 100
A country with a high urban percentage typically has extensive built-up areas and a large service sector. Rapidly rising urbanisation can bring challenges such as overcrowding and pressure on infrastructure.
城市化率高的国家通常建成区面积广阔、服务业庞大。城市化快速推进也可能带来过度拥挤和基础设施压力等挑战。
10. Time Zones and Longitude | 时区与经度
The Earth rotates 360 degrees in 24 hours, meaning it turns 15 degrees of longitude per hour. This is the basis of the world’s time zone system. Each 15° band broadly represents one hour of time difference from Greenwich Mean Time (GMT).
地球每24小时自转360度，即每小时转过经度15度。这是世界时区系统的基础。每15°经度区间大致代表与格林尼治标准时间（GMT）相差一个小时。
Time Difference (hours) = Longitude Difference ÷ 15
时差（小时） = 经度差 ÷ 15
Moving east, the time becomes later (add hours); moving west, the time becomes earlier (subtract hours). When using this in an exam, remember that some countries adjust boundaries for political or practical reasons, but the 15°/hour rule gives the theoretical time difference.
向东移动，时间变晚（小时数增加）；向西移动，时间变早（小时数减少）。在考试中应用时，要记住有些国家出于政治或实际原因调整了时区边界，但每15°差1小时的规则给出的是理论时差。
11. Temperature Statistics | 温度统计
Climate understanding begins with temperature calculations. The daily or monthly temperature range shows the variability of temperatures, while the mean temperature gives a general picture of warmth or cold.
对气候的理解始于温度计算。日较差或月较差显示温度的变化幅度，而平均温度则提供冷暖的总体状况。
Range = Tmax − Tmin
温度较差 = 最高温度 − 最低温度
Mean Temp = (Sum of all temperature readings) ÷ Number of readings
平均温度 = 温度观测值总和 ÷ 观测次数
For climate graphs, you often calculate the annual mean temperature by averaging the 12 monthly mean temperatures. Large annual temperature ranges typically indicate a continental interior location, while small ranges are common near coasts.
绘制气候图表时，通常将12个月的月平均温度相加后取平均值，即得到年平均温度。年温差大通常表明地处大陆内部，而年温差小则常见于沿海地区。
12. Rainfall Analysis and Climate Graphs | 降雨量分析与气候图
Total annual rainfall is simply the sum of the 12 monthly precipitation totals. This figure helps classify climates as arid, semi-arid, temperate, or tropical wet. More detailed analysis includes calculating the percentage of rain falling in the wettest season.
年总降雨量就是12个月的月降水量之和。这个数值有助于将气候划分为干旱、半干旱、温带或热带湿润气候。更细致的分析包括计算降雨最多季节占总雨量的百分比。
Total Rainfall = Σ Monthly Rainfall
总降雨量 = 各月降雨量之和
When constructing a climate graph, plot temperature as a line (left vertical axis) and precipitation as bars (right vertical axis). Knowing the formulas for mean, range, and totals allows you to interpret weather station data effectively and to compare different locations with confidence.
绘制气候图时，用曲线表示温度（左纵轴），用柱状表示降水（右纵轴）。掌握了平均值、较差和总量的计算公式，你就能有效解读气象站数据，并自信地比较不同地点的气候。
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