Return on Investment Calculator

ROI Formula: Measuring Total Gain or Loss

Return on investment compares how much value you gained to how much money you put in at the start. It is a simple percentage that answers: “How much did I make (or lose) relative to what I spent?”

Let:

• V_i = initial investment (starting value)
• V_f = final value (ending value)

The ROI formula is:

ROI = (Vf − Vi) / Vi × 100%

In MathML, this can be written as:

Interpretation:

• Positive ROI – the final value is higher than the initial investment (a gain).
• Zero ROI – the final value equals the initial investment (no gain or loss).
• Negative ROI – the final value is less than the initial investment (a loss).

ROI is easy to understand and works well for quick comparisons, but it does not say anything about how long it took to earn that return. For that, you need CAGR.

CAGR Formula: Converting Total Return into an Annual Rate

Compound annual growth rate (CAGR) answers a more time-aware question: “If my investment had grown at a steady rate each year, what annual rate would produce the same final value?”

Using the same notation as above and letting n be the number of years the investment was held, the CAGR formula is based on compound growth:

CAGR = (Vf / Vi)1/n − 1

In MathML form:

To convert CAGR to a percentage, multiply by 100%. A CAGR of 0.08 means an 8% average annual growth rate.

CAGR is especially useful when you want to compare investment options held for different lengths of time or when the timing of returns matters.

Worked Example: Calculating ROI and CAGR Step by Step

Suppose you invest $3,000 in a startup and sell your shares three years later for $5,000.

1. Calculate ROI

First, find the gain:

• Gain = $5,000 − $3,000 = $2,000

Then divide by the initial investment and convert to a percentage:

• ROI = ($2,000 / $3,000) × 100% ≈ 66.67%

This means your total return over the three-year period is about 66.67%.

2. Calculate CAGR

Now include time. Here, V_i = 3,000, V_f = 5,000, and n = 3 years.

• Step 1: Compute the ratio of final to initial value: 5,000 / 3,000 ≈ 1.6667.
• Step 2: Take the 1/3 power (the cube root) of this ratio: 1.6667^1/3 ≈ 1.184.
• Step 3: Subtract 1: 1.184 − 1 = 0.184.

So the CAGR is about 0.184, or 18.4% per year when expressed as a percentage.

This tells you that, even if actual yearly returns were uneven, they are equivalent to earning a steady 18.4% each year for three years.

ROI vs. CAGR: When to Use Each

ROI and CAGR describe the same investment from different angles. ROI focuses on the total outcome, while CAGR focuses on the average yearly pace of growth.

In practice, you will often look at both numbers together. For example, a project with a high ROI but very long holding period may have a modest CAGR once time is factored in.

Interpreting Your Results

Once you enter your values and run the calculator, consider the results in context:

• Compare ROI to your target – Is the total percentage gain or loss acceptable given the risk you took?
• Compare CAGR to benchmarks – How does the average annual rate stack up against alternatives, such as index funds, savings accounts, or borrowing costs?
• Look at sign and magnitude – A small positive ROI might not justify the time and risk, while a modest negative ROI could still be acceptable if it served a strategic purpose (for example, a marketing test).
• Consider inflation and taxes – The calculator shows a nominal return. After adjusting for inflation and taxes, your real return may be lower.

Remember that a higher ROI or CAGR is not automatically better. You should always weigh returns against risk, liquidity, and your broader financial goals.

Common Use Cases for ROI and CAGR

This calculator can be applied to many scenarios, not just stocks or funds:

• Business projects – Compare the return from different product launches, software tools, or process improvements.
• Real estate – Evaluate property purchases by including purchase price, closing costs, renovation expenses, and net sale proceeds.
• Marketing campaigns – Weigh the revenue generated by a campaign against the ad spend and creative costs.
• Equipment or technology – Measure time savings or extra revenue relative to the cost of new equipment.

In all cases, the quality of the result depends on how accurately you capture all relevant cash in and cash out in your initial and final values.

Assumptions and Limitations

The ROI and CAGR results from this calculator rely on several simplifying assumptions. Understanding these helps you interpret the numbers appropriately.

• No interim cash flows – The formulas assume there are no additional deposits, withdrawals, dividends, coupons, or rental income between the start and end points. If there are, those should be incorporated into the initial or final value, or a more advanced method such as internal rate of return (IRR) may be more suitable.
• Constant compounding for CAGR – CAGR treats growth as if it occurred smoothly at a single fixed annual rate, even though real investments often experience volatile, uneven returns.
• Nominal returns only – The calculator does not adjust for inflation, currency changes, or taxes. To estimate real, after-tax performance, you would need to make additional adjustments outside of this tool.
• Input quality – Results are only as accurate as the values you enter. Forgetting fees, maintenance costs, or transaction charges will typically overstate ROI and CAGR.
• Educational use – This calculator is meant for informational and educational purposes only and does not provide financial, investment, or tax advice. Always consider consulting a qualified professional before making significant decisions.

These limitations do not make ROI or CAGR useless; they simply mean the numbers should be one input into your decision-making rather than the sole deciding factor.

Further Reading

If you want to explore these concepts in more depth, look for materials from well-regarded financial education sources that cover topics such as:

• Formal definitions of return on investment and examples across different asset classes.
• How compound annual growth rate is derived from compound interest formulas.
• When to use more advanced measures like internal rate of return (IRR) or net present value (NPV).

Comparing multiple perspectives can help you develop a more complete understanding of how ROI and CAGR fit into long-term planning and project evaluation.