SME
Geographic Information Systems (GIS) · Problem type
Area of a buffer
Use this for “How much land lies within 100 m of a 2 km road?”
Chart
A = 2rL + πr²
A
=
2
×
100
×
2,000
+
π
×
100
2
A = 400,000 + 31,400 = 431,400 m²
The strip along the line is 2r wide; the two round ends make one circle.
This is an example. Type your own values to start a new problem.
A (m²)
=
2
×
r (m)
×
L (m)
+
π
(
r (m)
)
2
Formulas
A
=
2
×
r
×
L
+
π
×
r
2
431,415.9265
=
2
×
100
×
2,000
+
π
×
100
2
Assumptions
•
The buffer has round ends, so a line’s buffer is a strip 2r wide plus one whole circle.
•
The line is straight, or bends so gently that the strip’s corners do not overlap.
•
A point’s buffer is just the circle: set the line length to 0.
Step-by-step
WE KNOW
L = 2,000 m, r = 100 m
FIND
buffer area (A)
Step 1 · Find buffer area (A)
Use A = 2 × r × L + π × r²
A
strip
2
r
wide
runs
the
length
of
the
line,
and
the
two
half-circle
ends
make
one
circle.
A
=
2
×
100
×
2,000
+
π
×
100
2
2 × 100 × 2,000 = 400,000
π
×
100
2
=
31,415.9
400,000 + 31,415.9 = 431,415.9
A
=
431,415.9
m²
Check
Put the numbers back in. Both sides should match.
431,415.9
=
2
×
100
×
2,000
+
π
×
100
2
✓
Topic check
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