About the Continuous Compounding Calculator
Continuous compounding is the limit you reach when interest is added every instant instead of monthly or daily. The growth follows the number e. This calculator finds the final value from a starting amount, a yearly rate and a number of years, compares it with ordinary yearly compounding, shows the extra amount and the effective yearly rate, and gives the time to double. Type the starting amount, the yearly rate and the years and the continuous compounding appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Continuous Compounding Calculator
- 1Enter the starting amount, the yearly rate and the years.
- 2Pick the units or options from the menus if the continuous compounding tool offers them.
- 3Read the continuous compounding in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the continuous compounding
Finance students use it in option pricing and exponential growth, and engineers and scientists use the same formula for populations and decay.
The more often interest compounds, the closer the answer gets to the continuous value, but the gain is small: going from daily to continuous adds only a tiny amount. The big gain comes from the rate and the years.
How the continuous compounding is worked out
A = P × e^(r × t), where e is about 2.71828. The effective yearly rate is e^r − 1. The doubling time is ln 2 ÷ r. 1,000 at 5% for 10 years gives 1,000 × e^0.5 = 1,648.72. Yearly compounding gives 1,628.89, so continuous compounding adds about 19.83. The doubling time is 0.6931 ÷ 0.05 = 13.86 years.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Compares with yearly compounding
- Effective yearly rate
- Doubling time
Mistakes to avoid with continuous compounding
Enter the rate as a percent (5, not 0.05). And keep the time in years if the rate is a yearly rate. A negative rate is allowed and gives continuous decay.
On phone and computer
On a phone, type into the boxes one after another and read the continuous compounding underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the continuous compounding move. The continuous compounding calculator works the same on both.
Checking your continuous compounding by hand
A good habit is to test the continuous compounding calculator with a case you already know. 1,000 at 5% for 10 years gives 1,000 × e^0.5 = 1,648.72. Yearly compounding gives 1,628.89, so continuous compounding adds about 19.83. The doubling time is 0.6931 ÷ 0.05 = 13.86 years.
If your own figures give a surprising answer, repeat the working yourself: A = P × e^(r × t), where e is about 2.71828. The effective yearly rate is e^r − 1. The doubling time is ln 2 ÷ r. Small differences usually come from rounding, from mixing units, or from a typing slip in one of the inputs. Continuous growth is the limit of compounding more and more often, so compare it with the usual kind. Run the same numbers through the Compound Interest Calculator, discount a future sum with the Present Value and NPV Calculator, and ask how long growth takes with the Investment Time Calculator.
Features
- Enter the rate as percent
- Keep rate and time in the same unit
- Gain from continuous is small
- Clear messages when the continuous compounding inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate continuous compounding?
A = P × e^(r × t), where e is about 2.71828. The effective yearly rate is e^r − 1. The doubling time is ln 2 ÷ r. 1,000 at 5% for 10 years gives 1,000 × e^0.5 = 1,648.72. Yearly compounding gives 1,628.89, so continuous compounding adds about 19.83. The doubling time is 0.6931 ÷ 0.05 = 13.86 years.
What is the formula for continuous compounding?
A = P × e^(r × t), where e is about 2.71828. The effective yearly rate is e^r − 1. The doubling time is ln 2 ÷ r. The continuous compounding calculator applies it exactly and rounds only the displayed answer to six significant figures.
What is e?
A constant, about 2.71828, that arises from growth that compounds all the time.
Is continuous compounding used in real accounts?
Seldom. It is mostly a model in finance theory.
How long does money take to double?
About 0.693 divided by the rate, so 13.9 years at 5%.
Is this continuous compounding calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.