Free time: six days or ten, on the convention you declare

Name the events that start and stop the clock, the weekdays your convention counts and the excluded dates. The same fifteen dates read six chargeable days or ten by the weekdays alone.

Live result

Free time ran out, so your convention counts 6 chargeable days and your tiers total 91.5 unit.

last free date2026-01-06
first chargeable date2026-01-07

Widen the allowance or drop a counted weekday and the count moves with it.

The weekday grid

One cell per civil date

Try a convention

Named weekday shapes

Counted weekdays, 1 is Monday

The first day counted

This choice can move the count by a whole day.

Free days allowed3free days

The record editor takes the full range to 365.

Open the complete convention record

Every label, date, weekday, exclusion and rate on this page is an example so the page has something to draw.

The two events

Convention label

Event family

A name for the event pair; it selects no rule.

Trigger event label

Trigger event date

End event label

End event date

The calendar rule

Calendar rule label

The end date

Free days, full rangefree days

Dates you excluded

Excluded date 1

Date

Your class

Effect on the clocks

Excluded date 2

Date

Your class

Effect on the clocks

Excluded date 3

Date

Your class

Effect on the clocks

Excluded date 4

Date

Your class

Effect on the clocks

Your tiers

Your unit label

A unit label of your own.

Tier 1

From charge day

Through charge day

Rate

Type a plain decimal with up to twelve decimal places.

Tier 2

From charge day

Through charge day

Rate

Type a plain decimal with up to twelve decimal places.

Tier 3

From charge day

Upper boundary

Rate

Type a plain decimal with up to twelve decimal places.

The day census

Dates between the two events

Count: 15

Dates counted for free time

Count: 3

Dates counted for charge

Count: 6

Dates excluded

Count: 6

Free days consumed

Count: 3

Free days unconsumed

Count: 0

The day census	Count
Dates between the two events	15
Dates counted for free time	3
Dates counted for charge	6
Dates excluded	6
Free days consumed	3
Free days unconsumed	0

Your tiers

From: 1
Through: 2
Rate: 10.25
Days counted: 2
Subtotal: 20.5
Exact: $\frac{41}{2}$

From: 3
Through: 4
Rate: 15.5
Days counted: 2
Subtotal: 31
Exact: 31

From: 5
Through: open
Rate: 20
Days counted: 2
Subtotal: 40
Exact: 40

Tier	From	Through	Rate	Days counted	Subtotal	Exact
1	1	2	10.25	2	20.5	$\frac{41}{2}$
2	3	4	15.5	2	31	31
3	5	open	20	2	40	40

Total

Days counted: 6
Subtotal: 91.5
Exact: $\frac{183}{2}$

Every date, one row

2026-01-01

ISO weekday: 4
Selected: yes
Your exclusion: none
State: free counted
Ordinal: free 1
Tier: none
Amount: none

2026-01-02

ISO weekday: 5
Selected: no
Your exclusion: none
State: free excluded
Ordinal: none
Tier: none
Amount: none

2026-01-03

ISO weekday: 6
Selected: no
Your exclusion: none
State: free excluded
Ordinal: none
Tier: none
Amount: none

2026-01-04

ISO weekday: 7
Selected: yes
Your exclusion: Example free exclusion, free
State: free excluded
Ordinal: none
Tier: none
Amount: none

2026-01-05

ISO weekday: 1
Selected: yes
Your exclusion: none
State: free counted
Ordinal: free 2
Tier: none
Amount: none

2026-01-06

ISO weekday: 2
Selected: yes
Your exclusion: none
State: free counted
Ordinal: free 3
Tier: none
Amount: none

2026-01-07

ISO weekday: 3
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 1
Tier: 1
Amount: $\frac{41}{4}$

2026-01-08

ISO weekday: 4
Selected: yes
Your exclusion: Example charge exclusion, charge
State: charge excluded
Ordinal: none
Tier: none
Amount: none

2026-01-09

ISO weekday: 5
Selected: no
Your exclusion: Example combined exclusion, both
State: charge excluded
Ordinal: none
Tier: none
Amount: none

2026-01-10

ISO weekday: 6
Selected: no
Your exclusion: Example annotation only, neither
State: charge excluded
Ordinal: none
Tier: none
Amount: none

2026-01-11

ISO weekday: 7
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 2
Tier: 1
Amount: $\frac{41}{4}$

2026-01-12

ISO weekday: 1
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 3
Tier: 2
Amount: $\frac{31}{2}$

2026-01-13

ISO weekday: 2
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 4
Tier: 2
Amount: $\frac{31}{2}$

2026-01-14

ISO weekday: 3
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 5
Tier: 3
Amount: 20

2026-01-15

ISO weekday: 4
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 6
Tier: 3
Amount: 20

Date	ISO weekday	Selected	Your exclusion	State	Ordinal	Tier	Amount
2026-01-01	4	yes	none	free counted	free 1	none	none
2026-01-02	5	no	none	free excluded	none	none	none
2026-01-03	6	no	none	free excluded	none	none	none
2026-01-04	7	yes	Example free exclusion, free	free excluded	none	none	none
2026-01-05	1	yes	none	free counted	free 2	none	none
2026-01-06	2	yes	none	free counted	free 3	none	none
2026-01-07	3	yes	none	charge counted	charge 1	1	$\frac{41}{4}$
2026-01-08	4	yes	Example charge exclusion, charge	charge excluded	none	none	none
2026-01-09	5	no	Example combined exclusion, both	charge excluded	none	none	none
2026-01-10	6	no	Example annotation only, neither	charge excluded	none	none	none
2026-01-11	7	yes	none	charge counted	charge 2	1	$\frac{41}{4}$
2026-01-12	1	yes	none	charge counted	charge 3	2	$\frac{31}{2}$
2026-01-13	2	yes	none	charge counted	charge 4	2	$\frac{31}{2}$
2026-01-14	3	yes	none	charge counted	charge 5	3	20
2026-01-15	4	yes	none	charge counted	charge 6	3	20

Free days allowed

free days

Fromfree days

Tofree days

In steps offree days

It does not check the values in between.

No other integer in the range leaves the whole count of chargeable days at 6 days. Every admissible integer in this range was checked.

The answer	6 days
Values sampled	0 free days to 12 free days, 13 values, step 1 free day
Holds from	3 free days
Holds to	3 free days
Nearest value that changes it	2 free days and 4 free days
The answer there	7 days / 5 days

What an unchanged region does and does not prove is set out in a short lesson.

Every admissible integer in this range was checked. Values outside the range remain unchecked.

Here is the maths

The formula, in words

The first eligible date is the trigger date, or the one after it, as you declared. A date counts against free time when its weekday is one you counted and you have not excluded it from the free clock. After your allowance of free dates has counted, the first charge date is the next counted date you have not excluded from the charge clock. Every charge date takes the next ordinal, the ordinal falls in one of your tiers, and the tier rate is added as an exact fraction. Nothing is rounded until it is printed.

A worked example

The example runs from 2026-01-01 through 2026-01-15. It counts weekdays 1, 2, 3, 4 and 7, includes both event dates, and allows three free days.

The free dates are 2026-01-01, 2026-01-05 and 2026-01-06. The first counted charge date is 2026-01-07, and six charge dates remain in the event trace.

The date on 2026-01-08 is excluded from the charge clock. The dates on 2026-01-09 and 2026-01-10 do not count under the selected weekdays, while their typed annotations remain in the ledger.

2026-01-01

ISO weekday: 4
Selected: yes
Your exclusion: none
State: free counted
Ordinal: free 1
Tier: none
Amount: none

2026-01-02

ISO weekday: 5
Selected: no
Your exclusion: none
State: free excluded
Ordinal: none
Tier: none
Amount: none

2026-01-03

ISO weekday: 6
Selected: no
Your exclusion: none
State: free excluded
Ordinal: none
Tier: none
Amount: none

2026-01-04

ISO weekday: 7
Selected: yes
Your exclusion: Example free exclusion, free
State: free excluded
Ordinal: none
Tier: none
Amount: none

2026-01-05

ISO weekday: 1
Selected: yes
Your exclusion: none
State: free counted
Ordinal: free 2
Tier: none
Amount: none

2026-01-06

ISO weekday: 2
Selected: yes
Your exclusion: none
State: free counted
Ordinal: free 3
Tier: none
Amount: none

2026-01-07

ISO weekday: 3
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 1
Tier: 1
Amount: $\frac{41}{4}$

2026-01-08

ISO weekday: 4
Selected: yes
Your exclusion: Example charge exclusion, charge
State: charge excluded
Ordinal: none
Tier: none
Amount: none

2026-01-09

ISO weekday: 5
Selected: no
Your exclusion: Example combined exclusion, both
State: charge excluded
Ordinal: none
Tier: none
Amount: none

2026-01-10

ISO weekday: 6
Selected: no
Your exclusion: Example annotation only, neither
State: charge excluded
Ordinal: none
Tier: none
Amount: none

2026-01-11

ISO weekday: 7
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 2
Tier: 1
Amount: $\frac{41}{4}$

2026-01-12

ISO weekday: 1
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 3
Tier: 2
Amount: $\frac{31}{2}$

2026-01-13

ISO weekday: 2
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 4
Tier: 2
Amount: $\frac{31}{2}$

2026-01-14

ISO weekday: 3
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 5
Tier: 3
Amount: 20

2026-01-15

ISO weekday: 4
Selected: yes
Your exclusion: none
State: charge counted
Ordinal: charge 6
Tier: 3
Amount: 20

Date	ISO weekday	Selected	Your exclusion	State	Ordinal	Tier	Amount
2026-01-01	4	yes	none	free counted	free 1	none	none
2026-01-02	5	no	none	free excluded	none	none	none
2026-01-03	6	no	none	free excluded	none	none	none
2026-01-04	7	yes	Example free exclusion, free	free excluded	none	none	none
2026-01-05	1	yes	none	free counted	free 2	none	none
2026-01-06	2	yes	none	free counted	free 3	none	none
2026-01-07	3	yes	none	charge counted	charge 1	1	$\frac{41}{4}$
2026-01-08	4	yes	Example charge exclusion, charge	charge excluded	none	none	none
2026-01-09	5	no	Example combined exclusion, both	charge excluded	none	none	none
2026-01-10	6	no	Example annotation only, neither	charge excluded	none	none	none
2026-01-11	7	yes	none	charge counted	charge 2	1	$\frac{41}{4}$
2026-01-12	1	yes	none	charge counted	charge 3	2	$\frac{31}{2}$
2026-01-13	2	yes	none	charge counted	charge 4	2	$\frac{31}{2}$
2026-01-14	3	yes	none	charge counted	charge 5	3	20
2026-01-15	4	yes	none	charge counted	charge 6	3	20

The exact tier arithmetic counts days:

Tier 1, ordinals 1 to 2

Multiplication: $2 \times \frac{41}{4}$
Exact: $\frac{41}{2}$
Shown: 20.5

Tier 2, ordinals 3 to 4

Multiplication: $2 \times \frac{31}{2}$
Exact: 31
Shown: 31

Tier 3, ordinal 5 onward

Multiplication: $2 \times 20$
Exact: 40
Shown: 40

Total

Multiplication: $\frac{41}{2} + 31 + 40$
Exact: $\frac{183}{2}$
Shown: 91.5

Row	Multiplication	Exact	Shown
Tier 1, ordinals 1 to 2	$2 \times \frac{41}{4}$	$\frac{41}{2}$	20.5
Tier 2, ordinals 3 to 4	$2 \times \frac{31}{2}$	31	31
Tier 3, ordinal 5 onward	$2 \times 20$	40	40
Total	$\frac{41}{2} + 31 + 40$	$\frac{183}{2}$	91.5

What this does not model

It counts civil dates and nothing finer: an hour, a shift and a cutoff are all outside it. Editing a tier moves the total and moves no date at all.

Check it yourself

Set free days to 4 and then to 5. The count holds at 5 chargeable days across both. The fifth free day lands on 2026-01-08, a date you excluded from the charge clock, so it was never going to be a charge day. Moving the free boundary across it costs nothing. Narrow the bounds to 3 and 7 at a step of 1 and the flat step is two of the five values you check.

The kernel's own domain

Dates run from 1900-01-01 through 2100-12-31, with up to 731 dates between the events, free days from 0 through 365, up to 100 excluded dates, one through four tiers, and rates held as exact fractions to twelve decimal places.

Source

United States Federal Maritime Commission public detention and demurrage page. That published page establishes only that detention, demurrage and free time conventions exist.

The whole record prints. Your browser can save it as a PDF instead of printing it.

It describes the arithmetic consequences of one convention without determining which event family, trigger, end, weekday rule, exclusion class, free allowance, tier, rate or responsibility rule governs. This page never contains a real tariff table. It permanently refuses to validate an invoice, interpret a tariff or a contract, decide demurrage or detention liability, assign responsibility, invent a closure calendar, or choose between competing conventions. It counts the dates your own declaration counts, and it does not determine what anyone owes.

Free time: six days or ten, on the convention you declare

Name the events that start and stop the clock, the weekdays your convention counts and the excluded dates. The same fifteen dates read six chargeable days or ten by the weekdays alone.

Accepted inputs

Convention label: Fictional inspection convention
Event family: Cargo dwell
Trigger event label: Example availability event
Trigger event date: 2026-01-01
End event label: Example release event
End event date: 2026-01-15
Free days allowed: 3
Calendar rule label: Visitor selected civil weekdays
Counted weekdays, 1 is Monday: 1, 2, 3, 4, 7
The first day counted: The trigger date itself
The end date: Include the end date
Excluded date 1, Date: 2026-01-04
Excluded date 1, Your class: Example free exclusion
Excluded date 1, Effect on the clocks: free
Excluded date 2, Date: 2026-01-08
Excluded date 2, Your class: Example charge exclusion
Excluded date 2, Effect on the clocks: charge
Excluded date 3, Date: 2026-01-09
Excluded date 3, Your class: Example combined exclusion
Excluded date 3, Effect on the clocks: both
Excluded date 4, Date: 2026-01-10
Excluded date 4, Your class: Example annotation only
Excluded date 4, Effect on the clocks: neither
Your unit label: unit
Tier 1, From charge day: 1
Tier 1, Through charge day: 2
Tier 1, Rate: 10.25
Tier 2, From charge day: 3
Tier 2, Through charge day: 4
Tier 2, Rate: 15.5
Tier 3, From charge day: 5
Tier 3, Through charge day: open
Tier 3, Rate: 20
Every value came from the entered record: yes

All results

Calculation model

visitorTypedCivilDayConventionV1

Convention label

Fictional inspection convention

Event family

Cargo dwell

Trigger event label

Example availability event

Trigger event date

2026-01-01

End event label

Example release event

End event date

2026-01-15

Free days allowed

Calendar rule label

Visitor selected civil weekdays

Counted weekdays, 1 is Monday

1, 2, 3, 4, 7

The first day counted

The trigger date itself

The end date

Include the end date

Dates you excluded

2026-01-04, Example free exclusion, free; 2026-01-08, Example charge exclusion, charge; 2026-01-09, Example combined exclusion, both; 2026-01-10, Example annotation only, neither

free time ends

2026-01-06

first charge day

2026-01-07

the whole count of chargeable days

Free days consumed

Free days unconsumed

Your unit label

unit

Total

\frac{183}{2}

Total decimal

91.500000000000

Decimal places

Your tiers

From: 1
Through: 2
Rate: 10.25
Days counted: 2
Subtotal: 20.5
Exact: $\frac{41}{2}$
Rate exact: $\frac{41}{4}$
Subtotal decimal: 20.500000000000

From: 3
Through: 4
Rate: 15.5
Days counted: 2
Subtotal: 31
Exact: 31
Rate exact: $\frac{31}{2}$
Subtotal decimal: 31.000000000000

From: 5
Through: open
Rate: 20
Days counted: 2
Subtotal: 40
Exact: 40
Rate exact: 20
Subtotal decimal: 40.000000000000

Tier	From	Through	Rate	Days counted	Subtotal	Exact	Rate exact	Subtotal decimal
1	1	2	10.25	2	20.5	$\frac{41}{2}$	$\frac{41}{4}$	20.500000000000
2	3	4	15.5	2	31	31	$\frac{31}{2}$	31.000000000000
3	5	open	20	2	40	40	20	40.000000000000

The ledger

2026-01-01

ISO weekday: 4
Selected: yes
Class: none
Effect: none
State: free counted
Reasons: none
Free ordinal: 1
Free remaining: 2
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-02

ISO weekday: 5
Selected: no
Class: none
Effect: none
State: free excluded
Reasons: weekday not selected
Free ordinal: none
Free remaining: 2
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-03

ISO weekday: 6
Selected: no
Class: none
Effect: none
State: free excluded
Reasons: weekday not selected
Free ordinal: none
Free remaining: 2
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-04

ISO weekday: 7
Selected: yes
Class: Example free exclusion
Effect: free
State: free excluded
Reasons: typed date class
Free ordinal: none
Free remaining: 2
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-05

ISO weekday: 1
Selected: yes
Class: none
Effect: none
State: free counted
Reasons: none
Free ordinal: 2
Free remaining: 1
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-06

ISO weekday: 2
Selected: yes
Class: none
Effect: none
State: free counted
Reasons: none
Free ordinal: 3
Free remaining: 0
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-07

ISO weekday: 3
Selected: yes
Class: none
Effect: none
State: charge counted
Reasons: none
Free ordinal: none
Free remaining: 0
Charge ordinal: 1
Tier: 1
Amount exact: $\frac{41}{4}$

2026-01-08

ISO weekday: 4
Selected: yes
Class: Example charge exclusion
Effect: charge
State: charge excluded
Reasons: typed date class
Free ordinal: none
Free remaining: 0
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-09

ISO weekday: 5
Selected: no
Class: Example combined exclusion
Effect: both
State: charge excluded
Reasons: weekday not selected, typed date class
Free ordinal: none
Free remaining: 0
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-10

ISO weekday: 6
Selected: no
Class: Example annotation only
Effect: neither
State: charge excluded
Reasons: weekday not selected
Free ordinal: none
Free remaining: 0
Charge ordinal: none
Tier: none
Amount exact: none

2026-01-11

ISO weekday: 7
Selected: yes
Class: none
Effect: none
State: charge counted
Reasons: none
Free ordinal: none
Free remaining: 0
Charge ordinal: 2
Tier: 1
Amount exact: $\frac{41}{4}$

2026-01-12

ISO weekday: 1
Selected: yes
Class: none
Effect: none
State: charge counted
Reasons: none
Free ordinal: none
Free remaining: 0
Charge ordinal: 3
Tier: 2
Amount exact: $\frac{31}{2}$

2026-01-13

ISO weekday: 2
Selected: yes
Class: none
Effect: none
State: charge counted
Reasons: none
Free ordinal: none
Free remaining: 0
Charge ordinal: 4
Tier: 2
Amount exact: $\frac{31}{2}$

2026-01-14

ISO weekday: 3
Selected: yes
Class: none
Effect: none
State: charge counted
Reasons: none
Free ordinal: none
Free remaining: 0
Charge ordinal: 5
Tier: 3
Amount exact: 20

2026-01-15

ISO weekday: 4
Selected: yes
Class: none
Effect: none
State: charge counted
Reasons: none
Free ordinal: none
Free remaining: 0
Charge ordinal: 6
Tier: 3
Amount exact: 20

Date	ISO weekday	Selected	Class	Effect	State	Reasons	Free ordinal	Free remaining	Charge ordinal	Tier	Amount exact
2026-01-01	4	yes	none	none	free counted	none	1	2	none	none	none
2026-01-02	5	no	none	none	free excluded	weekday not selected	none	2	none	none	none
2026-01-03	6	no	none	none	free excluded	weekday not selected	none	2	none	none	none
2026-01-04	7	yes	Example free exclusion	free	free excluded	typed date class	none	2	none	none	none
2026-01-05	1	yes	none	none	free counted	none	2	1	none	none	none
2026-01-06	2	yes	none	none	free counted	none	3	0	none	none	none
2026-01-07	3	yes	none	none	charge counted	none	none	0	1	1	$\frac{41}{4}$
2026-01-08	4	yes	Example charge exclusion	charge	charge excluded	typed date class	none	0	none	none	none
2026-01-09	5	no	Example combined exclusion	both	charge excluded	weekday not selected, typed date class	none	0	none	none	none
2026-01-10	6	no	Example annotation only	neither	charge excluded	weekday not selected	none	0	none	none	none
2026-01-11	7	yes	none	none	charge counted	none	none	0	2	1	$\frac{41}{4}$
2026-01-12	1	yes	none	none	charge counted	none	none	0	3	2	$\frac{31}{2}$
2026-01-13	2	yes	none	none	charge counted	none	none	0	4	2	$\frac{31}{2}$
2026-01-14	3	yes	none	none	charge counted	none	none	0	5	3	20
2026-01-15	4	yes	none	none	charge counted	none	none	0	6	3	20

Sweep of Free days allowed

The assumption: Free days allowed
Values sampled: 0 to 12 free days, 13 values, step 1
The answer: 6 days
Holds across: 3 to 3 free days
Nearest change: 2 free days, where it becomes 7 days and 4 free days, where it becomes 5 days
Reading the boundary: The sweep samples only the values you entered. Between samples the answer is not checked, so read the boundary as observed, not proven.

Record fields

Calculation version: 1.0.0
Calculation trace: 1. Validate the declared labels, dates, weekday set, exclusions, tiers and exact rate strings.2. Scan eligible civil dates until the declared free day allowance has counted.3. Find the next selected date that the charge clock does not exclude.4. Rebuild every civil date from the trigger through the end event.5. Assign charge ordinals to contiguous tiers and add their exact fractions.
Source anchor: United States Federal Maritime Commission public detention and demurrage page. That published page establishes only that detention, demurrage and free time conventions exist.

The weekday grid

The day census

Your tiers

Total

Free days allowed

Here is the maths

The formula, in words

A worked example

What this does not model

Check it yourself

The kernel's own domain

Source

Related

Accepted inputs

All results

Sweep of Free days allowed

Record fields