Signature
r_bar = R / D; DAR = AR / r_bar
| Inputs | Definition | Unit |
|---|---|---|
R | Net patient service revenue earned over the period, gross patient service revenue less contractual allowances, the charity care provision and the provision for doubtful accounts, with capitation and premium revenue excluded; above zero | currency |
D | Number of calendar days in the period over which R is earned, 91 for the three months ending 30 June; above zero | days |
AR | Net patient receivables on the balance sheet at the end of the period, net of credit balances, allowances for uncollectible accounts, discounts for charity care and contractual allowances; zero or above | currency |
r_bar | Average daily net patient service revenue, R divided by D | currency per day |
|---|---|---|
DAR | Net days in accounts receivable, the net receivables balance expressed as days of average daily net patient service revenue | days |
Function
Net days in accounts receivable function for a provider paid claim by claim
Maps a provider's net patient receivables, its net patient service revenue and the calendar days of the revenue period to net days in accounts receivable, the receivables balance expressed as days of average daily net revenue. The measure belongs to providers paid claim by claim, under fee-for-service or case-based payment such as the case-weighted payment per case of HE-FM-CWT-002, where every episode of care becomes a receivable until it is collected. HE-FM-DAR-001 gives the measure and HE-CF-DAR-001 builds its denominator from monthly revenue and actual calendar days as HFMA MAP Key FM-1 requires. Split by payer group, the overall figure is the revenue-weighted mean of the groups' own figures, the weighted mean of HE-FM-CRAT-001 and of the first part of HE-FM-CWT-001 with daily revenue in place of member or case numbers, so it is not drafted again. Since the balance equals r_bar times DAR, the cash released when collection shortens is r_bar times the fall in days, and the annual cost of carrying the balance at a cost of capital i is i times the receivables balance, the same rate-times-balance product as the return R_t = r * B_t on the balance still tied up in HE-CF-ANLS-002. The article's other use of released cash, held as cash and divided by daily cash operating expenses to give extra days cash on hand, is an alternative to the saving, not an addition to it. DAR equals the mean time a unit of revenue waits for cash, the W of Little's law in HE-FM-DES-003, only in a steady state with constant daily revenue, where the closing balance equals the time-average balance (derived); away from that state the two differ. Notation follows the Days in Accounts Receivable article.
Computational function
Computational function: HFMA net days in accounts receivable from three monthly net revenues and their calendar days
Takes the net patient receivables at the end of a quarter, the net patient service revenue of each of its three months and the months themselves, and returns the calendar days of the quarter, its revenue, average daily net revenue and net days in accounts receivable. It counts the actual days of the three months, as HFMA MAP Key FM-1 requires, and then applies HE-FM-DAR-001, so its inputs are monthly ledger figures rather than the single R and D of the formula. The R and Python code take the last month reported and find the month lengths themselves, leap years included.
Inputs and outputs:
ARis the net patient receivables at the end of the quarter, zero or above, in currency;R_1,R_2andR_3are the net patient service revenue of the first, second and third month, in currency;d_1,d_2andd_3are the calendar days of those months;Dis the days of the quarter;Ris the quarter's net patient service revenue;r_baris average daily net revenue in currency per day;DARis net days in accounts receivable.Assumption: Monthly revenue and the receivables are both net, with capitation and premium revenue excluded, as in HE-FM-DAR-001, and the three months end with the month whose closing balance is AR.
Worked example (Quarter ending 30 June with rising monthly revenue): With an illustrative split of the article's USD 91.0 million into 28.0, 31.0 and 32.0 for April, May and June, the quarter has 91 days, r_bar is 1.0 and DAR is 55.0, as in the article. June's own daily rate of 32.0 over 30 days, 1.0667, would give 51.56 days (computed here for illustration). Money is in USD millions.
AR = 55; R_1 = 28; R_2 = 31; R_3 = 32; d_1 = 30; d_2 = 31; d_3 = 30; D = 91; R = 91; r_bar = 1; DAR = 55Worked example (Quarter ending 31 March 2026 with the same revenue): With illustrative revenue of 30.0, 30.0 and 31.0 for January, February and March 2026, the quarter has 90 days, so the same USD 91.0 million gives r_bar of 1.0111 and DAR of 54.40 (computed here for illustration). Money is in USD millions.
AR = 55; R_1 = 30; R_2 = 30; R_3 = 31; d_1 = 31; d_2 = 28; d_3 = 31; D = 90; R = 91; r_bar = 1.0111; DAR = 54.3956Excel:
=EOMONTH(ReportMonth,0)-EOMONTH(ReportMonth,-3)in QuarterCalendarDays and=NetReceivables/(SUM(MonthNetRevenue)/QuarterCalendarDays)in QuarterNetDaysInAR, with the first day of the last month reported in a cell named ReportMonth, the three monthly revenues in a range named MonthNetRevenue and the receivables in NetReceivables. For ReportMonth 1 June 2026 the first formula returns 91, the days of April, May and June.R:
fm1_days <- function(ar, rev, last_month) { first <- seq(as.Date(last_month), by = "-2 months", length.out = 2)[2]; end <- seq(as.Date(last_month), by = "month", length.out = 2)[2]; d <- as.numeric(difftime(end, first, units = "days")); c(D = d, r_bar = sum(rev) / d, DAR = ar / (sum(rev) / d)) }Called asfm1_days(55, c(28, 31, 32), "2026-06-01")it returns D = 91, r_bar = 1 and DAR = 55, and asfm1_days(55, c(30, 30, 31), "2026-03-01")it returns D = 90 and DAR = 54.3956.Python: With
import calendar,def fm1_days(ar, rev, year, last_month): d = sum(calendar.monthrange(year + (last_month-k-1)//12, (last_month-k-1) % 12 + 1)[1] for k in (2, 1, 0)); return d, sum(rev)/d, ar/(sum(rev)/d)Called asfm1_days(55, [28, 31, 32], 2026, 6)it returns (91, 1.0, 55.0), and asfm1_days(55, [30, 30, 31], 2026, 3)it returns 90 days and 54.3956 days.Test (Quarter ending 30 June): With NetReceivables 55, MonthNetRevenue 28, 31 and 32 and ReportMonth 1 June 2026, QuarterNetDaysInAR equals the article's 55.0 days. Expected result TRUE. FALSE shows a fixed 90-day quarter, which gives 54.40, or June's revenue and days alone, which gives 51.56, and doubling or halving the cell also gives FALSE. Excel check
=ABS(QuarterNetDaysInAR-55)<1E-9Test (Quarter ending 31 March 2026): With NetReceivables 55, MonthNetRevenue 30, 30 and 31 and ReportMonth 1 March 2026, QuarterNetDaysInAR equals 55 times 90 over 91, 54.3956 days. Expected result TRUE. FALSE shows a fixed 91-day quarter, which gives 55.0, or a leap-year February of 29 days, which gives 55.0 too, and doubling or halving the cell also gives FALSE. Excel check
=ABS(QuarterNetDaysInAR-55*90/91)<1E-9Common error (Dividing by the days of the last month only): Taking June's revenue of 32.0 over its 30 days as the daily rate gives 51.56 days in place of 55.0, 3.44 days lower, because a rising month is treated as the whole quarter (computed here for illustration).
Source: Healthcare Financial Management Association. MAP Keys, industry-standard revenue cycle KPIs. HFMA MAP Initiative web page, accessed 18 October 2026. FM-1, Average Daily Net Patient Service Revenue, the most recent three-month daily average using the number of days in the three months including the last month reported (91 days for the three months ending June 30).
D = d_1 + d_2 + d_3; R = R_1 + R_2 + R_3; r_bar = R / D; DAR = AR / r_bar
Try this function
Implementations
Excel
Net days in accounts receivable from named receivables, revenue and days
With net patient receivables in a cell named NetReceivables, net patient service revenue for the period in NetPatientRevenue and its calendar days in DaysInPeriod, the first formula returns r_bar in a cell named AvgDailyNetRevenue and the second returns DAR in a cell named NetDaysInAR. For the article's quarter the cells hold 55.0, 91.0 and 91 and return 1.0 and 55.0.
=NetPatientRevenue/DaysInPeriod; =NetReceivables/AvgDailyNetRevenue
Assumptions
Net receivables and net revenue on the same basis in days in accounts receivable
AR and R are both stated net, as in HFMA FM-1, which takes the net patient receivable on the balance sheet over average daily net patient service revenue. Gross receivables go over gross revenue and net over net, never one mixed with the other, because gross figures are valued at list charges that most payers do not pay in full.
Most recent three months and actual calendar days in the days in accounts receivable denominator
For FM-1, r_bar is the daily average of net patient service revenue over the most recent three months, using the actual number of calendar days in those months, so the three months ending 30 June use 91 days. A period of another length gives a figure that is not comparable with the HFMA measure.
Revenue earned claim by claim for days in accounts receivable
The formula assumes revenue that turns into receivables claim by claim, under fee-for-service or case-based payment. HFMA excludes capitation and premium revenue related to value-based or risk-based payer contracts from both the receivables and the revenue. Where a provider is paid fixed sums on account, as an NHS trust is paid one twelfth of its expected annual contract value each month under the NHS Standard Contract unless another proportion is agreed, the figure reflects contract timing rather than collection.
Steady daily revenue when days in accounts receivable are read as a collection period
DAR equals the time a unit of revenue waits for cash only when daily revenue is steady, the steady-state reading of Little's law in HE-FM-DES-003 (derived). With every dollar collected exactly 55 days after it is earned, the FM-1 figure is 55.0 at constant revenue and 56.96 when daily revenue grows by 0.2% a day (computed here for illustration), because the trailing three-month average understates current daily revenue. Growth raises the figure only while the collection lag is shorter than the 91-day window, and with every dollar collected after 120 days the same growth gives 116.69 (derived). HFMA describes FM-1 as a trending indicator.
Worked examples
Days in accounts receivable for the article's hospital quarter
The article's illustrative hospital, paid mainly per claim, earns net patient service revenue of USD 91.0 million in the quarter April to June (91 days) and holds net patient receivables of USD 55.0 million at 30 June. Average daily net revenue is USD 1.0 million, so the hospital holds 55.0 days of net revenue as receivables. Money is in USD millions.
AR = 55; R = 91; D = 91; r_bar = 1; DAR = 55
Days in accounts receivable of the patient balance payer group
Applied to the patient balance group of the article's table, with daily net revenue of USD 0.20 million, or USD 18.2 million over the 91 days, and USD 19.5 million in receivables, the group's own figure is 97.5 days. The public payer group (17.5 over 0.50) gives 35.0 days and commercial insurers (18.0 over 0.30) 60.0 days in the same way. Money is in USD millions.
AR = 19.5; R = 18.2; D = 91; r_bar = 0.2; DAR = 97.5
Days in accounts receivable after a shift in payer mix alone
In the article's step 3 the public payer's share of the USD 1.0 million daily revenue falls to 40% and the patient share rises to 30%, with every group collecting exactly as fast as before. Group receivables become 14.0, 18.0 and 29.25, USD 61.25 million in all, and the overall figure rises to 61.25 days with no change in billing, the revenue-weighted mean of the unchanged group days, the weighted-mean algebra of HE-FM-CRAT-001 with daily revenue in place of member numbers. Money is in USD millions.
AR = 61.25; R = 91; D = 91; r_bar = 1; DAR = 61.25
Days in accounts receivable after collection shortens to 45 days
In the article's step 4 better coding and fewer denials bring net days down to 45 at the same revenue, so receivables fall to USD 45.0 million and USD 10.0 million of cash is released, r_bar times the fall of 10 days. At an illustrative 6% a year the annual saving in carrying cost is USD 0.6 million, i times the released balance, the same rate-times-balance product as R_t = r * B_t in HE-CF-ANLS-002; alternatively, held as cash with daily cash operating expenses of USD 0.95 million, it adds about 10.5 days cash on hand. The two uses are alternatives, not additions. Money is in USD millions.
AR = 45; R = 91; D = 91; r_bar = 1; DAR = 45
Common errors
Net receivables divided by gross daily charges in days in accounts receivable
Dividing the article's USD 55.0 million of net receivables by illustrative gross daily charges of USD 2.5 million gives 22.0 days, 40% of the 55.0 net days, because list charges are far above what payers pay. Gross receivables go over gross revenue and net over net.
Reading a payer-mix shift as slower collection in days in accounts receivable
In the article's example the overall figure rises to 61.25 days against 55.0, 6.25 days or about 11.4% higher, when the public payer's share of revenue falls by ten points to 40%, although no payer group collects any more slowly. Comparing the group days, or their revenue-weighted mean at fixed revenue shares (the weighted-mean algebra of HE-FM-CRAT-001, there with member numbers as weights), separates the mix effect from the performance of the billing office.
A fixed 90-day denominator in place of calendar days in days in accounts receivable
For the quarter ending 30 June, dividing the USD 91.0 million of revenue by 90 days in place of the 91 calendar days gives r_bar of 1.0111 and 54.40 days in place of 55.0. HFMA counts the actual days of the three months, which differ between quarters and in leap years.
Taking a fall in net days from write-offs or allowances as faster collection
Raising the allowance for uncollectible accounts, or netting growing credit balances against debit balances, shrinks net receivables without any cash coming in. In the article's quarter an extra USD 5.0 million of allowance would take net days from 55.0 to 50.0 with nothing collected (computed here for illustration). HFMA's AR-1 ageing of billed receivables shows whether the fall came from collecting old accounts or from removing them, and its AR-9 net days in credit balance shows whether the credit balances netted off have grown.
Comparing days in accounts receivable of an NHS trust with hospitals paid per claim
Under the NHS Standard Contract each commissioner pays an NHS trust one twelfth of the expected annual contract value on the fifteenth day of each month, unless another day or proportion is agreed, payments on account that do not wait for claims. A trust's receivables from its main commissioners therefore reflect contract timing and in-year adjustments, and comparing its figure with that of a US hospital paid claim by claim says nothing about collection performance.
Sources
HFMA MAP Key FM-1 equation for net days in accounts receivable
Healthcare Financial Management Association. MAP Keys, industry-standard revenue cycle KPIs. HFMA MAP Initiative web page, accessed 18 October 2026. Financial Management group, Net Days in Accounts Receivable (A/R) (FM-1), whose equation divides net A/R from the balance sheet by average daily net patient service revenue from the income statement, describes the measure as a trending indicator of overall A/R performance, and defines net A/R as the net patient receivable on the balance sheet, net of credit balances, allowances for uncollectible accounts, discounts for charity care and contractual allowances for third-party payers.
HFMA MAP Key FM-1 definition of average daily net patient service revenue
Healthcare Financial Management Association. MAP Keys, industry-standard revenue cycle KPIs. HFMA MAP Initiative web page, accessed 18 October 2026. FM-1, Average Daily Net Patient Service Revenue, defined as the most recent three-month daily average of total net patient service revenue, with net patient service revenue equal to gross patient service revenue minus contractual allowances, minus charity care provision, then minus the provision for doubtful accounts. The definition counts the days in the three months including the last month reported, so the three months ending June 30 use April (30 days), May (31 days) and June (30 days), 91 days in all, and the FM-1 exclusions for both net A/R and revenue include capitation and premium revenue related to value-based or risk-based payer contracts.
NHS Standard Contract payments on account to NHS trusts
NHS England. 2026/27 NHS Standard Contract, Service Conditions (Full Length) (PRN02123). Version 1. London, NHS England; November 2025. SC36.12, under which each commissioner that has agreed an Expected Annual Contract Value must make payments on account to the provider, and SC36.13, under which, for an NHS Trust or NHS Foundation Trust, each commissioner pays on the fifteenth day of each month (or another day agreed in writing) one twelfth, or another proportion specified in Schedule 3D, of its Expected Annual Contract Value.
Canonical Identity
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