Sigma Calculator — 80+ Free Tools
Most textbook formulas assume tidy, equal payments. Real life is messier: a project pays $20,000 one year and $50,000 the next, a bonus lands in year three, a tax refund in year five. This calculator values uneven cash flows — up to four of them — by compounding each one forward to a common future date and adding up the results. Here is how to use it.
Step 1 — Enter the interest (discount) rate. Type the annual rate as a percentage. This is the rate at which money grows — your expected investment return, your cost of capital, or the hurdle rate for a project. The default is 6%.
Step 2 — Enter each cash flow amount and its year. For each of the up to four cash flows, type the dollar amount and the year it arrives (or was invested), measured from the same starting point. Years must be whole numbers, and they do not need to be consecutive — $6,000 in year 1 and $8,000 in year 5 is perfectly fine.
Step 3 — Click "Calculate Future Value" and read the results. The calculator shows the total future value measured at the year of the latest cash flow, plus a per-flow breakdown showing how much each individual cash flow has grown to. With the defaults — 6%, with $1,000 in year 1, $2,000 in year 2, $1,500 in year 3, and $3,000 in year 4 — the total is $8,028.22, built from $1,191.02 + $2,247.20 + $1,590.00 + $3,000.00.
Step 4 — Interpret the timing. Notice that the latest cash flow ($3,000 in year 4) earns no interest at all — it is already at the valuation date — while the earliest ($1,000 in year 1) grows for three full years. That asymmetry is the entire point of the tool: a dollar today and a dollar in three years are not worth the same, and the breakdown shows you exactly how much timing matters for your specific stream.
A cash flow is any movement of money — an investment deposit, a project's profit distribution, a loan repayment, a bonus. An annuity is the special case where the amounts are equal and evenly spaced, which is why annuities get their own shortcut formulas. An uneven (or non-level) cash flow stream has amounts that differ, or timing that is irregular, or both — and the only exact way to value it is to compound each flow individually and sum the pieces, which is precisely what this calculator does.
The engine underneath is compounding, the same force behind all time value of money mathematics: money available now can be invested, so a cash flow received earlier is worth more than the same nominal amount received later. The future value answers "what will this be worth at a later date?" while present value (or discounting) answers the reverse. Two close cousins appear constantly in project analysis: net present value (NPV), which discounts every flow — including the initial outlay — back to today and subtracts costs from benefits, and the internal rate of return (IRR), the discount rate that would make the NPV exactly zero. This calculator stays on the future-value side of that family, which is the natural view when you are asking "how much will I have?" rather than "what is it worth today?"
One design choice deserves emphasis: the valuation date. This calculator measures everything at T, the year of the latest cash flow. Each flow compounds for (T − t) years, where t is its own year — so the latest flow compounds for zero years and enters the total at face value. If you need the value at a different date — say, year 10 when the last flow arrives in year 4 — just compound the total forward: multiply by (1 + r)10−4. And if some of your "cash flows" are actually outflows (costs), enter them as negative amounts; the math handles signs naturally.
Each cash flow is grown forward from its own year to the valuation date T, and the grown amounts are summed:
FV = Σ CFi × (1 + r)(T − ti)
where CFi is cash flow i, ti is the year it occurs, r is the interest rate per year, and T is the latest year among all flows.
Worked example 1. Using the calculator's defaults — r = 6%, flows of $1,000 at year 1, $2,000 at year 2, $1,500 at year 3, $3,000 at year 4, so T = 4:
• CF1: $1,000 × (1.06)3 = $1,000 × 1.191016 = $1,191.02
• CF2: $2,000 × (1.06)2 = $2,000 × 1.1236 = $2,247.20
• CF3: $1,500 × (1.06)1 = $1,500 × 1.06 = $1,590.00
• CF4: $3,000 × (1.06)0 = $3,000 × 1 = $3,000.00
Total = $1,191.02 + $2,247.20 + $1,590.00 + $3,000.00 = $8,028.22. The four flows sum to $7,500 in nominal dollars, so compounding contributed $528.22 — and the breakdown shows nearly half of that came from the earliest $1,000 alone.
Worked example 2. A freelancer expects $5,000 in year 1, $5,000 in year 2, and $10,000 in year 5, and can earn 8%. Here T = 5:
• CF1: $5,000 × (1.08)4 = $5,000 × 1.360489 = $6,802.44
• CF2: $5,000 × (1.08)3 = $5,000 × 1.259712 = $6,298.56
• CF3: $10,000 × (1.08)0 = $10,000.00
Total = $6,802.44 + $6,298.56 + $10,000.00 = $23,101.00. Nominal inflows total $20,000, so four to five years of 8% growth added $3,101. Note the gap years 3 and 4 with no flows — the formula skips them effortlessly, which is exactly why uneven-flow tools beat annuity shortcuts for real-world streams.
A bakery owner considers a $90,000 oven upgrade expected to generate extra profits of $20,000 in year 1, $35,000 in year 2, and $50,000 in year 3. Her cost of capital is 10%, and she wants the future value of the inflows at year 3 to compare against the outlay grown at the same rate.
Compounding the inflows: $20,000 × (1.10)2 = $20,000 × 1.21 = $24,200; $35,000 × 1.10 = $38,500; $50,000 × 1 = $50,000. Total future value of inflows = $24,200 + $38,500 + $50,000 = $112,700. The $90,000 outlay, if instead invested at 10% for 3 years, would grow to $90,000 × 1.331 = $119,790. Hmm — wait. That comparison actually shows the project underperforming the hurdle: $112,700 < $119,790, a shortfall of $7,090 in year-3 dollars. The owner should renegotiate, find a cheaper oven, or reject the project — a conclusion she could never reach by just adding $20,000 + $35,000 + $50,000 = $105,000 and comparing it with $90,000, which misleadingly suggests a $15,000 profit. Timing-aware math reverses the naive answer, which is why finance professionals insist on compounding or discounting every flow.
After maxing his 401(k), an engineer invests variable bonuses into a taxable account earning about 7%: $6,000 in year 1, $6,500 in year 2, $7,000 in year 3, and $8,000 in year 5. What does he have at the end of year 5 (T = 5)?
• $6,000 × (1.07)4 = $6,000 × 1.310796 = $7,864.78
• $6,500 × (1.07)3 = $6,500 × 1.225043 = $7,962.78
• $7,000 × (1.07)2 = $7,000 × 1.1449 = $8,014.30
• $8,000 × (1.07)0 = $8,000.00
Total = $7,864.78 + $7,962.78 + $8,014.30 + $8,000.00 = $31,841.86. He deposited $27,500 nominally, so growth added $4,341.86. The breakdown also reveals something useful: the year-3 deposit of $7,000 outgrew the year-2 deposit of $6,500 in absolute terms ($8,014.30 vs. $7,962.78) because it was larger — but the year-1 $6,000 still beat both on a rate-of-growth basis, turning each dollar into $1.31. When bonuses are unpredictable, investing them immediately rather than letting them sit in cash is worth real money, and this is the receipt.
1. Compounding each flow for the wrong number of periods. The exponent is (T − ti) — the distance from the flow's year to the valuation date — not the flow's year itself. Growing the year-2 flow of the default example by (1.06)2 is correct only because T = 4; with T = 5 it would need (1.06)3. Always anchor on the valuation date first.
2. Mismatching the rate and the period length. Entering an 8% APR for flows dated in months without converting to a monthly rate overstates every compounded flow. If flows arrive monthly, use r = APR ÷ 12 and count months, not years, in the exponents.
3. Ignoring within-year timing. The calculator treats a "year 2" flow as arriving at the end of year 2. A flow that actually arrives at the beginning of year 2 earns roughly one extra year of interest — at 6%, that is 6% more on that flow. For large, early-year flows, state your convention explicitly.
4. Mixing nominal and inflation-adjusted flows. If your projected flows are in today's dollars (real) but your rate is nominal, you will overstate the future value. Either inflate the flows first or use a real rate: (1 + nominal) ÷ (1 + inflation) − 1. Pick one consistent basis for both.
5. Forgetting the valuation date is the latest flow's year. Adding a year-6 flow later means T moves to 6 and every earlier flow compounds one more year — the old total is not simply "plus the new flow." Recompute from scratch (or multiply the old total by 1 + r and add the new flow at face value).
For a single lump sum growing at a fixed rate, our Future Value Calculator is the simpler tool. You can also browse all Financial Calculators for present value, annuity, loan, and investment calculators.
This page provides a future value of uneven cash flows calculator. Inputs: annual interest rate r (percent, default 6) and up to four (amount, year) cash flow pairs; defaults $1,000 at year 1, $2,000 at year 2, $1,500 at year 3, $3,000 at year 4. Valuation date T is the latest cash flow year. Output: total future value = sum over i of CF_i × (1+r)^(T−t_i), plus a per-flow breakdown. Default result: $8,028.22 (components $1,191.02, $2,247.20, $1,590.00, $3,000.00). Flows are treated as end-of-period; negative amounts represent outflows; to value at a later date Y, multiply the total by (1+r)^(Y−T). This is a planning estimate, not financial advice.
Sources: standard time-value-of-money mathematics for uneven cash flow streams. This calculator is for planning only — actual returns vary, and investment decisions should consider risk, taxes, and fees. Last reviewed October 2026.
Enter up to four unequal cash flows with their years — find what the whole stream is worth at a future date with interest.
Enter up to four cash flow amounts and the year each one arrives, plus your annual interest rate. The calculator compounds each flow from its arrival year out to the latest year and adds them up — earlier payments earn interest for longer, so they contribute more.
Formula: FV = Σ CFᵢ × (1+r)^(T−tᵢ), where T is the latest year. Example: $1,000 in year 1, $2,000 in year 2, $1,500 in year 3 and $3,000 in year 4 at 6% → $1,000×1.06³ + $2,000×1.06² + $1,500×1.06 + $3,000 = $8,028.22 at year 4.
Compound each payment from the year it arrives to your target year, then add them up: FV = Σ CFᵢ × (1+r)^(T−tᵢ). The calculator above does it instantly.
The total worth of payments of different sizes arriving at different times, each grown with interest to a common future date — $8,028.22 for $1,000/$2,000/$1,500/$3,000 arriving in years 1–4 at 6%.
Yes — a payment arriving in year 1 compounds for three years while a year-4 payment earns nothing, which is why timing matters as much as the amounts.
Future value grows today's money forward with interest; present value discounts future money back. They are the same formula run in opposite directions.
Yes — any stream of unequal payments at different dates works, as long as you can state each amount and the year it arrives.