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IRR Calculator

Solves numerically for the discount rate at which the net present value of an initial investment and its subsequent cash flows equals zero, and reports the undiscounted gain and the number of sign changes (a warning for multiple IRRs).

When to use

You want the annualized (per-period) return implied by an investment's cash-flow pattern, e.g. to compare projects or check a fund's stated return.

Do not use when: Cash flows change sign more than once (multiple IRRs may exist; use npv at your hurdle rate), or there are only two values (use cagr).

Formula

Solve −initial_investment + Σ_{t=1..n} cash_flows[t] / (1 + IRR)^t = 0 for IRR by bisection on (−99 %, 1000 %)

Bisection to machine precision on the NPV function, which is guaranteed to converge when the series has one sign change (conventional investment). The IRR is a per-period rate and assumes interim cash flows are reinvested at the IRR.

Inputs

Parameter	Type	Unit	Required	Description
`initial_investment`	number		yes	Outlay at time 0, entered as a positive number. Range: > 0, ≤ 1000000000000000
`cash_flows`	number_list		yes	Net cash flow at the end of periods 1, 2, 3 … (negative values allowed).

Outputs

Output	Type	Unit	Description
`irr_percent`	number	% per period	Rate at which NPV = 0 (annual if the cash flows are yearly).
`net_undiscounted_gain`	number		Σ cash_flows − initial_investment (NPV at 0 %).
`total_cash_flows`	number		Σ cash_flows.
`number_of_periods`	integer		Length of cash_flows.
`sign_changes`	integer		Sign changes in the series (−investment, CF_1 … CF_n); more than 1 means several IRRs can exist.

Example

−1,000 then 500, 400, 300: {"initial_investment":1000,"cash_flows":[500,400,300]} → {"irr_percent":10.65,"net_undiscounted_gain":200,"total_cash_flows":1200,"number_of_periods":3,"sign_changes":1}

−10,000 then 3,000, 4,000, 5,000, 2,000: {"initial_investment":10000,"cash_flows":[3000,4000,5000,2000]} → {"irr_percent":15.32,"net_undiscounted_gain":4000,"sign_changes":1}

GET https://tttkmbb.com/api/v1/calculate/irr?initial_investment=1000&cash_flows=500%2C400%2C300

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/irr (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/irr · Markdown: https://tttkmbb.com/finance/irr.md · JSON definition: https://tttkmbb.com/finance/irr.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="irr"
OpenAPI operationId: calculate_irr
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Investopedia – Internal Rate of Return (IRR): Formula and Examples (reference)
Wikipedia – Internal rate of return (reference)

FAQ

Why can there be no IRR?

If the cash flows never turn positive (or the series never changes sign) NPV never crosses zero, so no rate satisfies the equation; the calculator returns CALCULATION_ERROR in that case.

IRR or NPV?

NPV measures value created at your required return and ranks mutually exclusive projects correctly; IRR is a convenient rate for comparing against a hurdle rate but can mislead when project sizes or timings differ.

Related calculators

NPV Calculator — Value of the same cash flows at a chosen rate.
CAGR Calculator — Return between a single start and end value.
ROI Calculator — Simple total return without timing.