A Duckworth Lewis calculator answers the question every rain-hit limited-overs match eventually poses: if the side batting second has lost overs, how many runs should they now need? The answer is not a simple pro-rata scaling of the first innings score, and understanding why is most of what this page is for.
Arb Digital publishes a free tools library, and this page sits in its sports section beside the net run rate calculator, which handles the tournament-table arithmetic that follows a result, and the cricket strike rate calculator for individual batting figures. This tool deals with the target itself.
An Honest Statement About What This Is
This section comes first because it changes how you should read every number below it.
The method used in professional cricket is the Duckworth-Lewis-Stern method, adopted by the International Cricket Council and described on the ICC's own page for Duckworth Lewis Stern rules and regulations. Under the ICC's playing conditions, revised targets in international matches are produced by official DLS software distributed by the ICC. That software, and the full underlying parameter set of the Professional Edition, are not published openly. Nobody outside the custodians of the method can reproduce an official DLS number from first principles.
What is public is the framework: the idea that a batting side's remaining scoring capacity can be expressed as a single resource percentage combining overs left and wickets in hand, and the arithmetic that turns two resource percentages into a revised target. That framework is what this page implements. The resource curve it uses is described explicitly in the formula section — it is this page's own smooth approximation of the shape a resource table has, not a copy of anyone's table.
So: the target arithmetic here is the real, published arithmetic. The resource percentages are an estimate. Expect a difference of several runs against an official figure, larger at low overs and high wicket counts where the real tables bend most sharply. If you have the official table to hand, switch on the override and type R1 and R2 in directly — the target the page then produces uses only the published formulas and is exact.
What This Duckworth Lewis Calculator Does
It takes both innings, not just the second. That matters, because interruptions to the first innings change how many resources the side batting first actually used, and a target computed as though they had a full innings will be wrong.
For each innings you enter the overs scheduled, the point at which play stopped, the wickets down at that moment, and how many overs were left when play resumed. From those it computes R1 and R2, the percentage of a full innings' scoring resources each side had available. It then applies the standard target rules, shows the par score to tie separately from the target to win, and reports the number of overs the chasing side actually receives.
The bars show R1, R2 and the resources lost between them, which is usually the clearest way to see whether a revision is mild or severe.
How to Use It
- Set the format first. It fills the scheduled-overs fields for both innings. Change them by hand if overs were cut before the toss.
- Enter innings one as it actually happened. If it ran to completion, set "overs bowled at interruption" equal to the scheduled overs and leave the resumption field at zero. That is the uninterrupted case and gives R1 of 100%.
- Enter innings two the same way. The wickets figure is the number down at the moment play stopped, not at the end.
- Check the overs-received figure in the grid. If it does not match what the umpires announced, one of your over entries is wrong.
- Use the override if you have the official table. Type R1 and R2 straight in and the page becomes a pure implementation of the published target formulas.
The Formula / How It's Calculated
Two formulas govern the target, and which one applies depends on a comparison, not on who batted first.
If R2 is less than or equal to R1 — the chasing side has fewer resources — the target is scaled down in proportion: Target = (S × R2 ÷ R1) rounded down, plus 1, where S is the first innings score. If R2 is greater than R1 — the chasing side has more resources, which happens when innings one was cut short and innings two was not — you cannot scale upwards proportionally, because a side that scored 200 in a curtailed innings would be credited with runs they never had a chance to make against a specific attack. Instead the surplus resource is valued at a fixed rate: Target = S + G50 × (R2 − R1) ÷ 100, rounded down, plus 1. G50 is a constant representing the average first-innings score in a full match; the ICC uses 245 for one-day internationals under the Standard Edition.
Resources themselves are computed by subtraction. A side starts with the resources of a full allocation, R(N, 0). When play stops with a overs left and w wickets down, and resumes with b overs left, the resources lost are R(a, w) − R(b, w). If play never resumes, b is zero and the whole of R(a, w) is lost.
The resource function on this page is R(u, w) = 100 × Z(w) × (1 − e−b(w)·u) ÷ D, with Z(w) = (1 − w ÷ 10)0.87, b(w) = 0.033 × (1 + 0.12w) and D chosen so that a full 50 overs with no wickets down returns exactly 100. The exponential shape reflects the real behaviour it is approximating: extra overs are worth a lot when you have few and progressively less when you have many, and wickets in hand both cap the total and change how fast that ceiling is approached. These parameters are this page's own, chosen to give a smooth, sensible curve. They are not the Duckworth-Lewis parameters.
Worked example, matching the values this page loads with. A 50-over match. Team 1 bats through all 50 overs and makes 250, so R1 = 100%. Team 2 is interrupted after 20 overs with 2 wickets down — 30 overs left — and returns to find only 15 overs left. For w = 2, Z = 0.80.87 = 0.8236 and b = 0.04092. R(30, 2) works out at 72.07% and R(15, 2) at 46.76%, so the resources lost are 25.31 points and R2 = 74.69%. Since R2 is below R1, the target is 250 × 0.7469 = 186.7, floored to 186 and increased by one: 187 to win from 35 overs, with 186 being the par score to tie.
Why Pro-Rata Scaling Is Wrong
The intuitive revision is to divide: if the chasing side gets 70% of the overs, give them 70% of the runs. Every version of the resource method exists because that answer is systematically unfair, and it is unfair in a direction most spectators guess wrong.
A side that knows in advance it has 35 overs bats differently from a side pacing itself for 50. It attacks earlier, accepts more risk, and scores at a higher rate per over. Overs are not interchangeable units of scoring — the last ten overs of an innings are worth far more runs than the middle ten, because a batting side spends the middle overs preserving wickets precisely so it can spend them later. Pro-rata scaling ignores that entirely and hands the chasing side a target that is too easy.
Wickets are the second half of the correction. A team 30 overs from the end with nine wickets standing is in a completely different position from a team 30 overs from the end with two, even though both have identical overs remaining. Any method that revises on overs alone can be gamed: a side chasing in doubtful weather would simply block, keep wickets, and wait for the rain. The resource surface makes that strategy expensive, because sitting on wickets while overs tick away burns resources either way.
The Cases That Trip People Up
Two situations produce results that look wrong at first glance and are not.
A target that goes up. If the first innings is cut short and the second is not, R2 exceeds R1 and the chasing side is asked for more than the first side scored. This is correct. The side batting first was interrupted in a way that stopped them using resources they had; the chasing side has those resources available. The G50 term prices the difference.
The par score during play. Broadcasters show a running par figure, which is the score the chasing side would need to be level if the match were abandoned at that instant. It is computed the same way, using the resources remaining at that moment. A side ahead of par is winning only in the sense that they would win an abandonment right now — it is not a prediction.
Match Formats Change the Constants
Everything above is written around the 50-over game because that is where the method originated, but the same machinery runs in Twenty20 with different numbers. The resource curve is steeper, because 20 overs is closer to the part of the curve where every over matters, and G50 is replaced with a format-appropriate average-score constant set in the relevant playing conditions rather than the 245 used for one-day internationals.
Domestic competitions set their own values, which is why a revised target in a county or state match can differ from what ICC constants would give for the same scoreline. The International Cricket Council publishes the regulations governing international fixtures; national boards publish their own.
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Browse the Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating the output as an official DLS figure — it is an estimate built on a published approach with a transparent approximation of the resource curve, and it will differ from the ICC software.
- Entering the wickets at the end of the innings — the model needs the wickets down at the moment play stopped, because that is when the resources were lost.
- Forgetting the first innings interruption — leaving R1 at 100% when innings one was itself curtailed produces a target that is too low, sometimes badly so.
- Adding one to the par score twice — the target already includes the extra run needed to win. The par figure in the grid is the score that ties.
- Using 245 for a Twenty20 match — G50 is a one-day international constant, and applying it to a short format overvalues surplus resources dramatically.
Related Free Tools From Arb Digital
The net run rate calculator handles the tournament table position that a revised result feeds into, and the cricket strike rate calculator covers individual batting rates. For the underlying arithmetic, the percentage calculator and the ratio calculator are both useful when you are checking resource proportions by hand. Everything else is in the free online tools hub.
Frequently Asked Questions
No. The professional method is the proprietary DLS system, and its full tables and software are distributed by the ICC rather than published openly. This page implements the standard published resource-percentage approach with its own transparent resource curve, so it will differ from an official figure and cannot be used to settle a match.
A single number combining overs remaining and wickets in hand that expresses how much of a full innings' scoring capacity a batting side still has. A full allocation with no wickets down is 100%, and it falls as overs are used or wickets fall.
Because the side batting first can lose resources too. If their innings was cut short while the chasing side gets a full one, the chasing side has more resources available, and the surplus is valued using the G50 constant and added to the first innings score.
Because overs are not equal. A side that knows it has fewer overs attacks from the start and scores faster per over, and wickets in hand change what a given number of overs is worth. Proportional scaling ignores both and produces targets that are too easy for the chasing side.
G50 is the assumed average first-innings score in an uninterrupted match, used only when the chasing side has more resources than the side batting first. The ICC uses 245 for one-day internationals under the Standard Edition. Twenty20 and domestic competitions set their own values in their playing conditions.
Switch the override on and enter R1 and R2 from the official resource table for your competition. The target arithmetic this page applies to those two numbers is the published arithmetic, so the result will be exact for the table you used.
The score the chasing side would need to be level if the match were abandoned at that instant, computed from the resources remaining at that moment. Being ahead of par means you would win an abandonment now; it is not a forecast of the finish.
This tool is an educational estimate of a rain-revised cricket target and is not an official Duckworth-Lewis-Stern calculation. Official targets in any competitive fixture are produced only by the software and playing conditions of the governing body for that competition, which are the sole authority.
