— Everyday Math
Growth Rate Calculator
Calculate growth three ways: simple percentage change, compound annual growth rate (CAGR), or average growth across a series. Enter the values to see the rate, total growth, period-by-period breakdown, and optional inflation-adjusted result.
Growth rate
50%
- Total change
- 50
- Start → end
- 100 → 150
— How it works
Simple growth = (end − start) ÷ start × 100 (the percentage change). CAGR = (end ÷ start)^(1 ÷ periods) − 1 — the constant rate that compounds from start to end over the periods.
Simple growth vs annualised growth
Over a single step, the growth rate is just the percentage change: subtract the start from the end, divide by the start, and multiply by 100. A value going from 100 to 150 has grown 50%. But over several periods that 50% is the total growth, not the yearly rate — and quoting it as if it were annual badly overstates the pace. The compound annual growth rate (CAGR) fixes that: it is the single steady rate that, compounded each period, turns the start into the end. That distinction — total versus annualised — is the one this calculator keeps front and centre.
Worked example — 100 grows to 150 over 5 years: Total growth = (150 − 100) ÷ 100 = 50%. CAGR = (150 ÷ 100)^(1 ÷ 5) − 1 = 8.45% a year — the steady rate that compounds to the same 150.
Why CAGR beats a simple average
It is tempting to annualise by dividing the total growth by the number of years — 50% over 5 years as “10% a year”. That is wrong, because growth compounds: 10% a year for 5 years would reach 161, not 150. CAGR accounts for the compounding, which is why it is the standard way to describe the growth of revenue, users, an investment or a population over time. It is also why CAGR is always a little lower than the naive average when growth is positive. In series mode the calculator takes a whole list of period values and returns the CAGR from first to last, alongside the actual growth between each step — which is rarely as smooth as the average suggests.
Real growth: stripping out inflation
A nominal growth rate can flatter: if a figure grew 8% but prices rose 3%, the real gain was closer to 5%. Enter an inflation rate under the advanced options and the calculator shows the real (inflation-adjusted) rate, computed properly as (1 + growth) ÷ (1 + inflation) − 1 rather than a simple subtraction. One guard applies throughout: the starting value must be positive, since growth and CAGR are measured relative to it, and a compound rate cannot be taken from a zero or negative base.
— Reader questions
How do I calculate a growth rate?
For a single period, use (end − start) ÷ start × 100 — the percentage change. From 100 to 150 that is 50%. Over multiple periods, use the CAGR instead, which annualises the growth.
What is CAGR and how is it calculated?
The compound annual growth rate is the steady yearly rate that turns the start into the end: CAGR = (end ÷ start)^(1 ÷ periods) − 1. For 100 to 150 over 5 years it is 8.45% a year — lower than the 50% total because growth compounds.
Why is CAGR lower than the total growth?
Because the total growth covers all the periods at once, while CAGR is the per-period rate. A 50% total over 5 years compounds at only about 8.45% a year. Annualising by simple division (50 ÷ 5 = 10%) overstates it, since it ignores compounding.
How do I find the average growth rate of a series?
Use series mode and list the value at each period. The calculator computes the CAGR from the first value to the last, and shows the growth between each consecutive pair so you can see how uneven it was.
What is real growth?
Real growth is the growth rate after removing inflation: (1 + nominal) ÷ (1 + inflation) − 1. If something grew 8% while inflation was 3%, the real growth was about 4.85%. Enter an inflation rate under the advanced options to see it.