Decline Curve Calculator
Forecast production decline using exponential or hyperbolic models.
About this calculator
This calculator applies the two classical Arps decline-curve models used throughout petroleum reserve estimation. Exponential decline follows q = qi x e^(-D x t), where Initial Production Rate (qi) and Annual Decline Rate (D) alone set the whole curve -- it's the more conservative model, since production falls off at a constant PERCENTAGE rate forever and never flattens. Hyperbolic decline instead follows q = qi / (1 + b x D x t)^(1/b), where Hyperbolic b Factor controls how much the decline rate itself SLOWS over time -- a higher b Factor produces a curve that flattens out more (a "long tail" of lower but persistent production), which is why hyperbolic forecasts generally project MORE Cumulative Production than an exponential forecast run with the same starting rate and decline percentage.
Cumulative Production sums estimated monthly output across the entire Forecast Period, so it rises with Initial Production Rate and Forecast Period and falls as Annual Decline Rate increases -- both trends hold whichever Decline Type is selected, even though the two models trace different shapes to reach their totals. Final Rate is the production rate at the very end of the Forecast Period, always scaling directly (and linearly) with Initial Production Rate for a fixed decline rate and forecast length, since neither decline model changes the SHAPE of the curve in response to the starting rate, only its overall height. Hyperbolic b Factor only affects the forecast when Decline Type is set to Hyperbolic -- it has no role at all in the Exponential model.
Inputs
Results
Final Rate
25.5 bbl/day
Cumulative Production
585,751 bbl
How to Use This Calculator
- Enter initial production rate (bbl/day) and annual nominal decline rate (%).
- Select decline type: exponential (conservative) or hyperbolic, and enter the hyperbolic b factor if applicable.
- Enter forecast period (years).
- Read Cumulative Production (a rough estimated ultimate recovery, or EUR, over the forecast window) and Final Rate at the end of the forecast period.
- Compare exponential vs. hyperbolic forecasts to understand reserve uncertainty range.
How the result changes with Forecast Period
| Forecast Period | Final Rate | Cumulative Production |
|---|---|---|
| 5 | 114.4 bbl/day | 478,895 bbl |
| 7.5 | 54 bbl/day | 551,469 bbl |
| 15 | 5.7 bbl/day | 609,594 bbl |
| 25 | 0.3 bbl/day | 616,101 bbl |
What each input means
- Initial Production Rate
- Initial production rate at time zero.
- Annual Decline Rate
- Annual nominal decline rate.
- Decline Type
- Decline model type. Exponential is conservative.
- Hyperbolic b Factor
- Hyperbolic exponent (b). Only used for hyperbolic decline.
- Forecast Period
- Number of years to forecast.
How this is calculated
Worked example, using the default values
- Identify Input Parameters5 parametersInitial Production Rate = 500, Annual Decline Rate = 30, Decline Type = 0, Hyperbolic b Factor = 1, Forecast Period = 10 = 5 input(s) provided
- Calculate Final RateFinal Rate25.5 = 25.5
- Calculate Cumulative ProductionCumulative Production585751 = 585751
- Calculate Total DeclineTotal Decline94.9 = 94.9
- Calculate Average RateAverage Rate160.4 = 160.4
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does a higher Hyperbolic b Factor increase Cumulative Production for the same starting rate and decline percentage?
A higher Hyperbolic b Factor makes the decline curve flatten out more over time -- the production rate keeps falling, but at a progressively slower percentage rate rather than the constant percentage rate of an exponential decline. That flatter "long tail" means more oil or gas is still being produced late in the forecast, which adds up to more total Cumulative Production over the same Forecast Period.
Why is Exponential decline called the more conservative model?
Exponential decline assumes production falls at a CONSTANT percentage rate forever, with no flattening -- this generally produces the LOWEST reasonable Cumulative Production estimate compared to hyperbolic models with any positive Hyperbolic b Factor, which is why engineers often use it as a conservative floor for reserve estimates rather than an optimistic case.
Does Hyperbolic b Factor do anything when Decline Type is set to Exponential?
No -- Hyperbolic b Factor only enters the calculation when Decline Type is Hyperbolic; the Exponential model's formula, q = qi x e^(-D x t), has no b term at all. You can leave Hyperbolic b Factor at any value while using Exponential decline without changing the forecast.
Why does Final Rate always scale directly with Initial Production Rate?
Both decline models multiply Initial Production Rate by a decay factor that depends only on Annual Decline Rate, Decline Type, Hyperbolic b Factor, and elapsed time -- never on the starting rate itself. Doubling Initial Production Rate therefore exactly doubles Final Rate (and every point along the curve) for the same decline settings, since the SHAPE of the decline is independent of how large the well started out.
What does Monthly Decline actually represent?
It's the equivalent MONTHLY percentage decline implied by Annual Decline Rate, which this calculator treats as a NOMINAL (continuously-compounding) annual decline constant everywhere else in the model -- for exponential decline, Monthly Decline is 1 - e^(-Annual Decline Rate/12), the nominal-annual-to-nominal-monthly conversion consistent with the q = qi x e^(-D x t) curve itself, and for hyperbolic decline it's simply Annual Decline Rate divided by 12. It's provided as a reference figure some operators track separately from the annual rate, not a distinct input to the forecast.
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