Exponential growthThe J-shaped curve. The population grows faster and faster.
Logistic growthThe S-shaped curve. Growth slows, then levels off.
TimeThe level axis. Time runs from left to right.
Population sizeThe upright axis. Higher means more individuals.
Reading the S curve 5
Carrying capacityThe largest population the environment can sustain.
Slow startThe population is small, so it grows slowly at first.
Rapid growthThe curve is steepest here. The population is growing fastest.
Growth slowsGrowth slows as the population nears its carrying capacity.
Levels offThe population stays near its carrying capacity.
How this list was compiled: Every name checked on 2026-10-03 in two independent sources. (1) Nature Education Knowledge (Scitable), How Populations Grow: The Exponential and Logistic Equations, by John Vandermeer, 2010, https://www.nature.com/scitable/knowledge/library/how-populations-grow-the-exponential-and-logistic-13240157/ : exponential and logistic growth of a population over time, the carrying capacity, a logistic curve that looks exponential while the population is small and levels off as it becomes large, a crowded population that grows more slowly. (2) Wikipedia: Exponential growth (the J-shaped exponential curve and the S-shaped logistic curve), Logistic function, Carrying capacity, Population growth, Population dynamics, https://en.wikipedia.org/wiki/Logistic_function : population size N, carrying capacity K, growth that decreases as the population approaches its carrying capacity and then levels off. (3) Alberta Education, Biology 30 (2009), read by full-text search on archive.org, https://archive.org/details/biology3008albe : logistic growth forms an S-shaped curve that begins with slow growth, steepens to exponential growth and levels off at the carrying capacity. (4) A Biology 20-30 school text (2007), read by full-text search on archive.org, https://archive.org/details/Biology-20-30 : the lag phase, the initial stage of slow growth. (5) The Nature of Life (1995), read by full-text search on archive.org, https://archive.org/details/isbn_9780070507579 : the J-shaped curve of exponential growth and the S-shaped curve of logistic growth. Licence: own work
The drawing: Drawn for this site on 2026-10-03 from plain geometry. The curves are computed from an exponential and a logistic function; nothing is traced or copied. Licence: own work
How it works
These population growth curves are labeled twice. First, two graphs side by side: exponential growth and logistic growth. Then one logistic curve drawn large, with its carrying capacity and four stretches named.
Read the full guide
Two curves
Both graphs plot population size against time. One curve climbs faster and faster: exponential growth, the J shape. The other rises, bends and flattens: logistic growth, the S shape.
The S curve
A logistic curve has a slow start, then rapid growth in the middle. Growth slows as the curve nears the dashed line, and the population levels off there. The dashed line, marked K, is the carrying capacity.
The shape names are accepted too: J-shaped curve and S-shaped curve.
Questions and answers
What is the difference between exponential and logistic growth?
Exponential growth keeps speeding up, so its graph is a J-shaped curve. Logistic growth begins the same way, slows as the population nears its carrying capacity and then levels off, so its graph is an S-shaped curve.
What is carrying capacity?
The carrying capacity is the largest population of a species that an environment can sustain with the food, space and other resources it has. On the graph it is the level the S-shaped curve flattens toward, written K.
Where can I drag the correct label under each graph to identify the type of population growth shown?
Here, with taps in place of drags. Both graphs are this site's own chart. Press Quiz me on Two curves, then tap the box under the graph that matches each name.
Why does logistic growth level off?
In a crowded population each individual has less space and fewer resources, so the population grows more slowly. Once it reaches the carrying capacity of its environment, it stays near that level.