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A buffer marks the ground within a distance of a feature: a circle of pi r squared around a point, a corridor twice the distance wide along a line.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to build buffers around points and lines, find their areas, and estimate what lies inside them.
You can overlay layers and measure the areas that result. This lesson adds distance: a buffer is the area within a set distance of a feature, and it becomes a new layer that can itself be measured and overlaid.
| Term | What it means |
|---|---|
| Buffer | The zone within a set distance of a feature. |
| Buffer distance | How far the buffer reaches from the feature. |
| Corridor | The buffer along a line, with rounded ends. |
| Multiple ring buffer | Several buffers at set distances, forming nested bands. |
| Setback | A rule keeping one use a minimum distance from another. |
| Service area | The area a facility can reach, by straight line or by road. |
A buffer marks all the ground within a buffer distance of a feature.
Another way: picture
Picture tying a string of a set length to a stake and walking all the way around, keeping it tight: the path marks a circle, the buffer of the stake. Now slide the stake along a straight fence; the string sweeps out a long strip with round ends, the buffer of the fence.
Another way: steps
Accessibility is always access for someone, to something, by a permitted mode, at a specified time. A circle measures straight-line proximity, not whether a person can pass through a locked gate, cross a river or arrive while a facility is open. Start by stating the travel budget and purpose, then select suitable network edges and destinations. Join destination attributes by stable IDs, and filter availability before computing routes. Include waiting and transfer costs where they apply. Verify that modeled junctions really connect and that one-way or mode restrictions are respected.
For a fictional library, one route takes 7 minutes along a path plus 6 minutes waiting and 4 minutes crossing a ferry: 17 minutes. Another route around the shore takes 14 minutes. The least-time route is the longer-looking shore route, assuming these are the only feasible alternatives. If the budget is 15 minutes, it qualifies and the ferry route does not. Adding a buffer cannot make that comparison because the relevant costs are times and restrictions.
To compare library locations, first attach opening hours, then compute time-based service areas over valid routes, then overlay those areas with residential reporting units. Use a buffer as a quick distance screen only when its purpose is explicit. If a service area intersects half of a block polygon, half of the residents need not live there. An area-weighted estimate assumes uniform population within that block. State that assumption, compare it with a safer finer dataset if available, and avoid releasing individual locations. Access can also depend on mobility, fees and opening hours missing from the supplied layers. A defensible answer selects an operation chain for the stated question and names those exclusions.
A buffer of $r$ around a point is a circle of area $\pi r^2$. Because the radius is squared, doubling the distance quadruples the area: a one-kilometer buffer covers about $3.14$ square kilometers, a two-kilometer buffer about $12.57$.
That makes buffer rules sensitive. Raising a setback from a thousand feet to two thousand keeps four times as much land clear around each site.
A buffer of $r$ along a straight line of length $L$ is a rectangle $L$ long and $2r$ wide, with a half circle at each end. Its area is $2rL + \pi r^2$.
For long lines and short distances, the ends barely matter, so $2rL$ is a good estimate. A ten-kilometer road buffered by a kilometer covers $20$ square kilometers plus about $3.14$ for the ends.
A multiple ring buffer draws several distances at once: within one, two and three kilometers of an airport, for example. Each band is a ring whose area is the difference between two circles.
The band from one to two kilometers covers $\pi(2^2 - 1^2) = 3\pi \approx 9.42$ square kilometers, three times the inner circle.
Buffer distances are often in meters or feet, and areas wanted in square kilometers or acres. A circle of $300$ m covers $\pi \times 90000 \approx 282700$ square meters, which is about $0.28$ square kilometers.
Convert once, carefully: a square kilometer is a million square meters, and a square mile is 640 acres.
A buffer measures straight-line distance, as the crow flies. People travel on roads, so a store one kilometer away across a river may be five kilometers by car.
Network analysis measures distance along roads instead, giving a service area shaped by the street network rather than a neat circle. Buffers are quicker; networks are more realistic.
Many laws are buffers: wells must be a set distance from septic systems, wind turbines from homes, liquor stores from schools. A GIS turns each rule into a buffer and overlays it with parcels to show what land is left.
In 2020, Colorado's oil and gas regulators adopted a default setback of 2,000 feet between new wells and homes, up from 500. Buffers made the debate concrete: they showed how much land each proposed distance would close to drilling.
The U.S. Department of Agriculture measures food access by buffering supermarkets. In its Food Access Research Atlas, a city neighborhood counts as low access when many residents live more than a mile from one; in the country, more than ten miles.
Overlaying those buffers with census tracts and income shows where people have far to go for fresh food.
Checking an answer. A circle's area is a bit over three times the radius squared. A corridor's area is a bit over its length times its width.
Using $\pi r^2$ is allowed because every point within $r$ of a center forms a circle. Using length times $2r$ is allowed because a straight line's buffer is a rectangle that width across, plus ends.
Multiplying by density is allowed as an estimate when people are spread roughly evenly; where they are not, finer data replaces it.
In 1854, the physician John Snow mapped cholera deaths in London and found them clustered around a water pump on Broad Street. Distance from the pump, the idea behind a buffer, pointed to the water as the source.
Epidemiologists still buffer sources of illness, from contaminated wells to industrial sites, to see who lives nearby.
A buffer drawn in degrees of latitude and longitude is not a circle on the ground. Because a degree of longitude shrinks toward the poles, a buffer of one degree around a point in Alaska is a tall, narrow oval, much wider in kilometers north and south than east and west.
The fix is the coordinates lesson's: buffer in a projected system measured in meters, such as the local UTM zone or state plane, or use a geodesic buffer, which measures true distance over the Earth's surface. For buffers of hundreds of kilometers, such as the range of a radar or an aircraft, only a geodesic buffer is accurate.
A quick check catches the slip: measure the buffer's width in two directions. If north and east disagree, the buffer was drawn in degrees. Redraw it in a projected system before measuring anything inside it, or every area and count will be off.
The most common slip is using the circumference, $2\pi r$, instead of the area. Another is forgetting to square the radius, or leaving out pi.
A third is buffering a line by the distance on one side only, giving half the width. A fourth is adding the areas of overlapping buffers, counting shared ground twice.
Buffers turn distance into area, and area can be overlaid, measured and mapped. The next unit leaves the map for the sky: remote sensing gathers the raster layers that so many buffers and overlays depend on.
Oil and gas wells in Colorado's Front Range often stand near subdivisions. For years the state required new wells to be at least 500 feet from homes; in 2020 its oil and gas commission adopted a default setback of 2,000 feet, with exceptions.
GIS analysts on all sides buffered every home in the affected counties at each proposed distance and overlaid the buffers with land where drilling was possible. Because area grows with the square of the radius, quadrupling the setback distance made each home's buffer sixteen times larger, and dissolved buffers of neighboring homes covered much of the suburbs.
The maps did not settle the argument, but they made clear what each number would mean on the ground, which is what buffers are for.
The U.S. Department of Agriculture's Food Access Research Atlas buffers every supermarket in the country. Census tracts where many residents live beyond a mile of one in cities, or beyond ten miles in rural areas, and where incomes are low, are marked as low income and low access, often called food deserts.
Health departments, grocers and nonprofits use the map to decide where to open stores, run mobile markets or fund transit routes.
Critics note what buffers leave out: whether residents have cars, whether the store is affordable, and whether a mile across a highway is really walkable. Network analysis along streets, and surveys of residents, fill some of those gaps.
It is easy to reach for the first circle formula that comes to mind, the circumference, or to multiply pi by the radius without squaring it. But a buffer is an area: pi times the radius squared, which grows with the square of the distance.
For corridors, the slip is buffering one side only; a buffer reaches the distance on both sides, so the corridor is twice the distance wide.
A well is buffered by $3$ km. Write the area.
$\pi \times 3^2$
A circle.
Evaluate the area.
$9\pi \approx 28.27\ \text{km}^2$
Square kilometers.
Name the circumference slip.
$2\pi \times 3 \approx 18.85$
A length, not an area.
Say what doubling the distance does.
$4 \times 28.27 \approx 113$
The area quadruples.
A $10$ km road is buffered by $1$ km. Find the width.
$2 \times 1 = 2\ \text{km}$
Both sides.
Find the straight part.
$10 \times 2 = 20\ \text{km}^2$
A rectangle.
Find the rounded ends.
$\pi \times 1^2 \approx 3.14$
Two halves.
Add the parts.
$23.14\ \text{km}^2$
The whole corridor.
Say when to skip the ends.
$\text{long roads, short distances}$
They are small.
A clinic is buffered by $2$ km, where density is $1500$ per square kilometer. Find the area.
$\pi \times 2^2 \approx 12.57$
Square kilometers.
Multiply by the density.
$12.57 \times 1500 \approx 18850$
People.
Name the unsquared slip.
$\pi \times 2 \times 1500 \approx 9425$
Half the true count here.
State the assumption.
$\text{even density}$
Rarely exact.
Say how to improve it.
$\text{overlay census blocks}$
Finer counts.
Say what a road network would show.
$\text{fewer people in reach}$
Trips longer than straight lines.
Write the area.
$\pi \times 5^2$
A circle.
Evaluate the area.
$25\pi \approx 78.54\ \text{km}^2$
Square kilometers.
Compare with the square slip.
A GIS draws a buffer of $10$ km around a well. About what area does the buffer cover, in square kilometers?
Complete the worked solution: a straight pipeline $16$ km long is buffered by $1.5$ km on each side, and homes stand at about $40$ per square kilometer. Ignoring the ends, find the corridor's width, its area, and the homes inside it.
Find the corridor's width.
$\text{two} \times \text{distance} =$ b
Both sides.
Find the corridor's area.
$\text{width} \times \text{length} =$ a
A long rectangle.
Find the homes inside.
$\text{area} \times \text{density} =$ n
Homes per square kilometer.
Say who would use this.
$\text{the regulator and the operator}$
Safety and notice.
Match each buffer to the shape it makes.
| a circle | a corridor with rounded ends | a ring surrounding a shape | nested bands of distance | |
|---|---|---|---|---|
| a buffer around a well | ||||
| a buffer along a highway | ||||
| a buffer around a lake | ||||
| buffers at one, two and three kilometers from an airport |
A GIS buffers a straight road $10$ km long by $1$ km. Fill in the area of the straight part, the area of the two rounded ends together, and the total, in square kilometers, to two decimals.
| area | |
|---|---|
| straight part (km²) | |
| two rounded ends (km²) | |
| whole corridor (km²) |
A straight road is $25$ km long. Ignoring the rounded ends, write the area of its buffer, in square kilometers, as a function of the buffer distance $x$ in kilometers.
Answer:
A health department buffers a clinic by $2$ km. The area around it has about $1500$ people per square kilometer. About how many people live within the buffer?
Answer: people
Suppose a city bars new liquor stores within $250$ m of any school. It has $12$ schools whose buffers do not overlap. How much land do the buffers cover, in square kilometers?
Answer: unit: m2 / km2
A fictional island has 2 proposed evening study centers. Students need a center reachable within 20 minutes on permitted walking routes. The supplied layers include center hours, paths, locked gates, pedestrian ferries with waiting times and aggregate student counts by block. Which analysis is justified?
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A straight road is $25$ km long. Ignoring the rounded ends, write the area of its buffer, in square kilometers, as a function of the buffer distance $x$ in kilometers.
Answer:
You can work with buffers. Explain why doubling a buffer distance around a point quadruples its area.
26. Your turn: a buffer of $5$ km surrounds a sensor. What area does it cover?, step 3
$25$
Pi left out.