What does CAGR stand for?

CAGR stands for compound annual growth rate. It is the smoothed annualized return that links a beginning value to an ending value over a selected period.

How is CAGR calculated?

CAGR is calculated as (ending value divided by beginning value) raised to the power of 1 divided by total years, minus 1. This tool also supports an extra month field for partial-year periods.

What is the difference between CAGR and absolute return?

Absolute return compares ending value with beginning value across the whole period, while CAGR expresses the same change as a smoothed annual rate.

There is no universal good CAGR. The answer depends on the asset class, risk taken, fees, taxes, inflation, and the time period being compared.

§ Tools / Series 03 · Personal finance · Return analysis

CAGR calculator

Q: When should I not use CAGR?

CAGR is not the right metric for irregular cash flows with deposits and withdrawals. In those cases, XIRR or money-weighted return is usually more appropriate.

Q: Can CAGR be negative?

Yes. If the ending value is below the beginning value, the implied CAGR is negative. If the ending value falls to zero, the limiting case is -100%.

The inverse-direction calculator. Compound interest asks “given a rate, what's the future value?” — this one asks “given the actual beginning and ending values, what annual rate connects them?” Closed-form, three real inputs, the same transparency layer as every other calculator in the suite.

§ Inverse direction

cagr = (ending / beginning)^{(1 / period)} − 1 — solved directly, no iteration. The companions (absolute return, gain/loss, value multiple, doubling years) are derivatives of the same multiple. Period months are first-class, so 7y 3m is exact; zero ending values are handled cleanly as −100%; and beginning vs ending units scale independently, so 1 lakh → 2 crores works without manual normalization.

Real inputs

±400

bps scenarios

±2y

Period sensitivity

7y 3m

Partial-year exact

Methodology

§ Start with a preset

Three baseline cases — including the realistic loss scenario most CAGR calculators omit.

Inputs

Independent units for beginning vs ending · partial-year periods · everything recomputes instantly.

Currency

Workbooks Individual+

01Beginning value

Amount

Unit

Independent of the ending unit.

02Ending value

Amount

Unit

Independent of the beginning unit — lakh → crore is fine.

03Holding period

Years

yrs

Months

0–11 · combined as years + months / 12.

Total

10.000 y

Compound annual growth rate

7.1773%

Over 10 years, $100 grew to $200 — an annualized rate of 7.18%. The absolute return was 100.00%.

Value multiple2.00×

Gain / loss+$100

Absolute return100.00%

Doubling time at this rate10.00 y

Beginning value

$100

100 × ones

Ending value

$200

200 × ones

Total period

10.000 y

10y 0m

Rule-of-72 estimate

10.03 y

vs exact 10.00 y

CAGR / absolute

0.718

smoothing factor vs avg/yr

Status

computed

methodology v1

§ Smoothed growth path

The CAGR curve — not the actual price path

Each marker is the value at year y, computed as beginning × (1 + cagr)^y. Real markets are messier. The headline rate is correct; this curve is a decoration.

Year	Smoothed value	Cumulative return	vs beginning
Y0 · start	$100	0.00%	1.000×
Y1	$107	7.18%	1.072×
Y2	$115	14.87%	1.149×
Y3	$123	23.11%	1.231×
Y4	$132	31.95%	1.320×
Y5	$141	41.42%	1.414×
Y6	$152	51.57%	1.516×
Y7	$162	62.45%	1.625×
Y8	$174	74.11%	1.741×
Y9	$187	86.61%	1.866×
Y10 · endpoint	$200	100.00%	2.000×

§ Period sensitivity

What if the period were 1 or 2 years longer or shorter?

Same beginning, same ending — recomputed at nearby periods. Catches off-by-one-year framing (was it 9 or 10 years?).

-2 y

8.00 y

9.05%

CAGR

-1 y

9.00 y

8.01%

CAGR

-0.5 y

9.50 y

7.57%

CAGR

Base

10.00 y

7.18%

CAGR

+0.5 y

10.50 y

6.82%

CAGR

+1 y

11.00 y

6.50%

CAGR

+2 y

12.00 y

5.95%

CAGR

§ Scenario ending values

What would the ending value be at nearby CAGRs?

Beginning held constant, period held constant, CAGR shifted by ±100 / 200 / 400 bps.

Shift	CAGR	Ending value	Multiple	vs actual
-400 bps	3.18%	$137	1.37×	$-63.3
-200 bps	5.18%	$166	1.66×	$-34.3
-100 bps	6.18%	$182	1.82×	$-17.9
Base	7.18%	$200	2.00×	—
+100 bps	8.18%	$219	2.19×	+$19.5
+200 bps	9.18%	$241	2.41×	+$40.6
+400 bps	11.18%	$289	2.89×	+$88.5

§ Formula trace

every output, derived

beginning = 100 × ones = 100.00 USD
ending = 200 × ones = 200.00 USD
total_period_years = 10 + 0/12 = 10.0000 y
multiple = ending / beginning = 2.000000×
cagr = (ending / beginning)^(1 / period) − 1 = (2.0000)^(1/10.0000) − 1 = 7.1773%
absoluteReturn = multiple − 1 = 100.0000%
gainLoss = ending − beginning = 100.00 USD
doublingYears = ln(2) / ln(1 + cagr) = 10.000 y

§ Input audit

no input silently ignored

beginningUnitused

beginningValueused

currencyused

endingUnitused

endingValueused

periodMonthsused

periodYearsused

§ Warnings

CAGR is a smoothed rate — it ignores volatility, drawdowns, and the actual path between beginning and ending.
CAGR is the wrong tool for irregular cash flows (deposits + withdrawals along the way). Use XIRR for those.

§ Golden references · locked in tests

Four fixtures pin the engine. The last one — beginning in lakhs, ending in crores — exists specifically to prove independent unit scaling works without manual normalization.

100 → 200 · 10 y

7.1773%

100 → 50 · 5 y

−12.9449%

100 → 100 · 10 y

0.0000%

1 L → 2 cr · 10 y

69.8646%

§ Inverse direction · sibling tools

Compound interest — given a rate, what future value? →Lump sum investment →SIP calculator →Fixed deposit calculator →FD vs stock market returns →

§ Same engine, headlessly

The closed-form CAGR solve, the period sensitivity, the bps scenarios, and the smoothed growth path are all reachable as a stateless REST endpoint and an MCP tool. Workbook CRUD is authenticated and stored under calculator_id=cagr. Unknown inputs are rejected with 422.

POST/api/v1/financial-calculators/cagr/calculate

POST/api/v1/financial-calculators/cagr/run

GET/api/v1/financial-calculators/cagr/schema

GET/api/v1/financial-calculators/cagr/defaults

GET/api/v1/user/financial-calculator-workbooks?calculator_id=cagr · individual+

MCP toolcalculate_cagr

methodology_version = financial-calculators.v1 · canonical = /en/tools/cagr-calculator

§ FAQ

Five things worth knowing

Q01What does CAGR actually stand for, and how is it different from the percentage I see in my brokerage?+

CAGR is the compound annual growth rate — the single smoothed rate at which the beginning value would have grown to the ending value, year after year. Your brokerage often shows absolute return (ending / beginning − 1), which makes a 5-year and a 15-year double look identical at "+100%". CAGR annualizes both so they are comparable: a 5-year double is 14.87% CAGR; a 15-year double is 4.73% CAGR.

Q02Can CAGR be negative?+

Yes — and that is exactly the "Half in 5y" preset. A portfolio that fell from 100 to 50 over 5 years has a CAGR of −12.9449%. The math is the same in both directions; the calculator surfaces a warning that doubling time is undefined for non-positive rates.

Q03My period is 7 years and 3 months, not a round number. Does that matter?+

Yes. Period months are first-class here, not optional. total_period_years = years + months / 12, so 7y 3m becomes 7.25 and the CAGR is computed exactly — not rounded to "about 7 years". The period-sensitivity table also shows what the rate would be at nearby periods so you can sanity-check off-by-one framing.

Q04When should I not use CAGR?+

Three cases. (1) Irregular cash flows along the way — use XIRR; CAGR assumes no contributions or withdrawals between the endpoints. (2) Sub-1-year holdings — annualizing a 3-month return overstates the rate; report absolute return instead. (3) Path-dependent reasoning — CAGR is smoothed, so it tells you nothing about the volatility, drawdowns, or sequence of returns. The headline rate is correct; the smoothed growth curve is decorative.

Q05Why is independent unit scaling its own feature?+

"1 lakh grew to 2 crores" is a natural way for people to describe a real result. Most calculators force you to normalize first (which is where off-by-100× mistakes happen). Here, beginning_unit and ending_unit are independent, so lakh → crore works directly and the formula trace shows both expansions before the math runs.