Formulas Guide

All formulas in this topic follow the order of operations as outlined in http://en.wikipedia.org/wiki/Order_of_operations. All numbers use the period (.) as the decimal separator, and apostrophes (') for digit grouping, if any digit grouping is used.

INT() means to round the number down to the nearest integer. INT(6.8) = 6
ROUND() means to round to the nearest integer. ROUND(6.8) = 7, ROUND(6.2) = 6, and ROUND(6.5) = 7.

Table of Contents:

* Points and Newb Protection
* Planet sizes and colonies
* Espionage
* Costs
* Mine Production/Consumption
* Build speed of buildings/ships/research
* Distances, Missiles, Expeditions
* Ship speed and flight times
* Deuterium costs for all flights
* Moons and Sensor Phalanx
* Combat and Resource capture
* Speed universes

Points:
You get 1 point for every 1000 resources spent on completed ships, buildings, research, and defense, with the following restrictions:
-Deuterium used in construction and research does count towards points; however deuterium spent fueling ships, powering a Sensor Phalanx, powering a Fusion Reactor, or viewing the galaxy does not.
-If you lose something through fleet attack, Interplanetary Missile attack, colony abandonment, etc. you also lose the points that you had for that something.
-Resources spent on deconstruction does NOT give you points; in fact, you lose points based on the building you deconstructed.

Points are updated via live statistics, when you gain something, you gain points, when you lose something, you lose the points.

Other types of points:
Research points
You get one research point for every research level that you complete for all technologies.

For example, if you have combustion drive level 5 and energy tech level 4, you will have 9 research points in total (so one for each level of combustion (5) and one for each level of energy (4))

Fleet points
You get one fleet point for every ship that you construct, with no matter attributed to what type of ship it is, whether it is as inexpensive as a Solar Satellite (SS) or as expensive as a Deathstar (DS).

For example, if your fleet consists of 300 SS and 2 DS, you will have 302 fleets points, just if you have 100 SS, 2000 Light Fighters and 100 Battleships, you will have 2200 fleet points.

Newb Protection:
If you have:
Less than 5'000 points: You can't attack players with more then 500% of your own points or less then 20% of your own points. Those people can't attack you either.

More than 5'000 points: You can't attack anybody who has less than 20% of your score and is under 5'000 points, and they can't attack you. You can attack everybody else, and they can attack you.

More than 25'000 points: You can attack everybody who has more then 5'000 points and those people can attack you too.

So if you have 4'200 points, you can attack or be attacked by someone with as little as 4'200 * 0.2 = 840 points, or as much as 4'200 * 5 = 21'000 points.

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Planet sizes:
Position 1: average: 64, 60% between 48 and 80 fields

Position 2: average: 68, 60% between 53 and 83 fields

Position 3: average: 73, 60% between 54 and 82 fields

Position 4: average: 173, 60% between 108 and 238 fields

Position 5: average: 167, 60% between 95 and 239 fields

Position 6: average: 155, 60% between 82 and 228 fields

Position 7: average: 144, 60% between 116 and 173 fields

Position 8: average: 150, 60% between 123 and 177 fields

Position 9: average: 159, 60% between 129 and 188 fields

Position 10: average: 101, 60% between 79 and 122 fields

Position 11: average: 98, 60% between 81 and 116 fields

Position 12: average: 105, 60% between 85 and 129 fields

Position 13: average: 110, 60% between 60 and 160 fields

Position 14: average: 84, 60% between 42 and 126 fields

Position 15: average: 101, 60% between 54 and 149 fields

The field numbers are possibilities, as derived from a statistical analysis of actual ingame results. Different numbers are always possible. ;)

The above data is not relevant for universe 42 and the named unis due to changes in the colonization rules. Attempts to calculate a new table are under way at Needed: colony sizes in uni 42.

Planet Fields:
INT(((Planet Size in km) / 1000) ^ 2)

There is no field limit on a moon.

Maximum number of available colonies:
In universes 42 and 44+:
Max Colonies = INT(((Level of Astrophysics) + 1) / 2)

In all other universes there is a hard limit of 8 colony slots.

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Espionage:
Number of probes to see X level of information:
X + (Y * ([(your Espionage Technology) - (your opponent's Espionage Technology)] ^ 2))
If a player has an active Technocrat then add 2 to the appropriate Espionage Technology.
If your Espionage Technology is higher than your opponent's, then Y is -1. If your opponent's is higher, then Y is 1, and if both are equal, Y is 0.

X = 2 for resources, activity, and ships
X = 3 for resources, activity, ships, and defense
X = 5 for resources, activity, ships, defense, and buildings
X = 7 for resources, activity, ships, defense, buildings, and research

You always get resources and activity no matter how many probes you send. If an espionage mission gets counterespionaged, the espionage report is still sent even if the espionaging fleet is destroyed.

Example:
You have Espionage Technology level 11, your opponent has level 12, and you want to see up to buildings when you espionage your opponent. You would send
5 + (1 * ((11 - 12) ^ 2))
5 + (1 * ((-1) ^ 2))
= 6 probes to get the wanted information.

Here's how many probes one should send to get up to research based on various differences of enemy Espionage Technology relative to yours:

* -3 Difference : 1 probe
* -2 Difference : 3 probes
* -1 Difference : 6 probes
* 0 Difference : 7 probes
* +1 Difference : 8 probes
* +2 Difference : 11 probes
* +3 Difference : 16 probes

Also, as you develop your Espionage Technology, you can find out more about incoming foreign fleets:
Level 2 lets you see how many ships are coming.
Level 4 also displays which types of ships are in the fleet.
Level 8 shows you how many of each ship type are in the fleet as well.

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Costs:
Per Level:
INT((Base Costs) * (Cost Increase Factor) ^ (level - 1))

Cumulative:
INT((Base Costs) * (1 - (Cost Increase Factor) ^ level) / (1 - (Cost Increase Factor)))
Note: Cumulative costs may be approximate because of the rounding used in the per level costs.

Cost Increase Factors:
Metal Mine, Deuterium Synthesizer, Solar Plant: 1.5
Crystal Mine: 1.6
Astrophysics (universes 42 and 44+ only): 1.75
Fusion Reactor: 1.8
Graviton Technology: 3
All other buildings and researches: 2

A list of base costs can be found at All Buildings, Researches, Fleets, and Defences.

Example:
Cost to build a level 15 Metal Mine:
Metal:
INT(60 * 1.5 ^ (15 - 1))
= 17'515 metal
Crystal:
INT(15 * 1.5 ^ (15 - 1))
= 4'378 crystal

Cumulative cost of a level 15 Metal Mine:
Metal:
INT(60 * (1 - 1.5 ^ 15) / (1 - 1.5))
= 52'427 metal
Crystal:
INT(15 * (1 - 1.5 ^ 15) / (1 - 1.5))
= 13'106 crystal

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Production per Hour:
Metal Mine:
30 * (level) * 1.1 ^ (level) metal
Crystal Mine:
20 * (level) * 1.1 ^ (level) crystal
Deuterium Synthesizer:
(10 * (level) * 1.1 ^ (level)) * (1.28 - 0.002 * (max temperature)) deuterium
To calculate mine production with an active Geologist, multiply the result by 1.1.
Solar Plant:
20 * (level) * 1.1 ^ (level) energy
Fusion Reactor:
30 * (level of Fusion Reactor) * (1.05 + (level of Energy Technology) * 0.01) ^ (level of Fusion Reactor)
Solar Satellites:
INT(max temperature / 4) + 20 energy per satellite, up to a maximum of 50 energy per satellite
To calculate energy production with an active Engineer, multiply the result by 1.1.

Storage Capacity:
100'000 + 50'000 * INT(1.6 ^ (level))

Example:
Storage capacity of a level 12 metal storage:
100'000 + 50'000 * INT(1.6 ^ 12)
100'000 + 50'000 * (281)
= 14'150'000 metal

Storages are changed in universes 42 and 44+, but it is unknown at this time if there is an actual formula behind the numbers. Here is a table outlining the changes:

Level Costs Redesign Capacity Old Capacity
0 0 10'000 100'000
1 1'000 20'000 150'000
2 2'000 40'000 200'000
3 4'000 75'000 300'000
4 8'000 140'000 400'000
5 16'000 255'000 600'000
6 32'000 470'000 900'000
7 64'000 865'000 1'400'000
8 128'000 1'590'000 2'200'000
9 256'000 2'920'000 3'500'000
10 512'000 5'355'000 5'550'000
11 1'024'000 9'820'000 8'850'000
12 2'048'000 18'005'000 14'150'000
13 4'096'000 33'005'000 22'600'000
14 8'192'000 60'510'000 36'100'000
15 16'384'000 110'925'000 57'700'000
16 32'768'000 203'350'000 92'300'000
17 65'536'000 372'785'000 147'650'000
18 131'072'000 683'385'000 236'200'000
19 262'144'000 1'297'589'000 377'850'000
20 524'288'000 2'296'600'000 604'550'000

Hourly Consumptions:
Metal Mine:
10 * (level) * 1.1 ^ (level) energy
Crystal Mine:
10 * (level) * 1.1 ^ (level) energy
Deuterium Synthesizer:
20 * (level) * 1.1 ^ (level) energy
Fusion Reactor:
10 * (level) * 1.1 ^ (level) deuterium

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Construction times:
Buildings, in hours:
((metal + crystal) / 2'500) * (1 / ((level robotic factory) + 1)) * (0.5 ^ (level nanite factory))

Ships and Defense, in hours:
((metal + crystal) / 5'000) * (2 / ((level shipyard) + 1)) * (0.5 ^ (level nanite factory))

Research Time, in hours:
(Metal + Crystal) / (1'000 * (1 + (Research Lab level)))
If you have an active Technocrat, multiply the result by 0.75.

To convert from hours to hours, minutes, and seconds, first take the decimal part of the hours and multiply it by 60 to get the minutes, then take the decimal part of the minutes and multiply that by 60 to get the seconds.
Note: If converting to hours, minutes, and seconds, make sure you use INT on the seconds, since each unit's build time is never more precise than whole seconds. Also, each unit takes at least one (1) second to build.

Example:
Build time of a level 6 Robotics Factory:
((12'800 + 3'840) / 2'500) * (1 / ((5) + 1)) * (0.5 ^ (0))
6.656 * (1 / 6) * 1
= 1.10933... hours
0.10933... * 60 = 6.56 minutes
INT(0.56 * 60) = 33 seconds
So the build time is 1hour 6minutes 33seconds

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Distances:
Same planet/moon/df:
5
In system:
1'000 + (5 * (Number of Planets))
Between Sytems:
2'700 + (95 * (Number of Systems))
Between Galaxies:
20'000 * (Number of Galaxies)

Missiles
Silo capacity
Capacity = 10 * (Level of Missile Silo)
Each Anti-Ballistic Missile takes 1 slot. Each Interplanetary Missile takes 2 slots.

Interplanetary Missiles:
Range, in systems:
(Impulse Drive level) * 5 - 1
Speed, in seconds:
(Number of Systems) * 60 + 30
You cannot send these missiles over galaxies.

Expeditions:
Maximum number of concurrent expeditions = INT((Level of Expedition Technology) ^ (1 / 2))
An expedition can hold at the slot 16 for 1 hour increments up to your current level of Expedition Tech.
In universes 42 and 44+, Astrophysics is used for the formula, but it is otherwise unchanged.

So, if you have level 6 Expedition Technology you would be able to send only INT(6 ^ (1 / 2)) = INT(2.449...) = 2 expeditions at the same time, and each would be able to hold for 1, 2, 3, ..., or 6 hours.

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Actual Ship Speed:
Actual Speed = (Base Speed) * (1 + ((Drive Level) * (Drive Bonus Factor)))

Drive Bonus Factor is 0.1 if the ship is using a Combustion Drive, 0.2 if using an Impulse Drive, and 0.3 if using a Hyperspace Drive.

A table of base speeds can be found at Drives FAQ.

Example:
A Small Cargo with Impulse Drive level 7 would have an actual speed of:
10'000 * (1 + (7 * 0.2))
10'000 * (1 + 1.4)
10'000 * 2.4
= 24'000

Flight Times, in seconds:
Same planet/moon/df
10 + ROUND[35'000 / % * (5'000 / speed) ^ (1 / 2)]
In System:
10 + ROUND[35'000 / % * ((1'000'000 + (number of planets) * 5'000) / speed) ^ (1 / 2)]
Between Systems:
10 + ROUND[35'000 / % * ((2'700'000 + (number of systems) * 95'000) / speed) ^ (1 / 2)]
Between Galaxies:
10 + ROUND[35'000 / % * (((number of galaxies) * 20'000'000) / speed) ^ (1 / 2)]

Example:
1 Deathstar from 3:22:1 to 3:23:1 at 100% speed, Hyperspace Drive at level 7 (310 speed)
10 + ROUND(35.000 / 100 * ((2'700'000 + (1) * 95'000) / 310) ^ (1 / 2)
10 + ROUND(350 * 94.95329922...)
=33244 seconds, or 9hours 14minutes 4seconds

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Deuterium Costs for Flights:
Fleets of one ship type
Same planet/moon/df
1 + ROUND[Fuel * (0.005 / 35) * (% / 100 + 1) ^ 2]
In system:
1 + ROUND[Fuel * ((1 + 0.005 * (Number of planets)) / 35) * (% / 100 + 1) ^ 2]
Between Systems:
1 + ROUND[Fuel * ((2.7 + 0.095 * (Number of systems)) / 35) * (% / 100 + 1) ^ 2]
Between Galaxies:
1 + ROUND[Fuel * ((20 * (Number of galaxies)) / 35) * (% / 100 + 1) ^ 2]
Fuel is the total fuel usage of the ships.

Example:
1 Large Cargo from 3:22:1 to 3:22:2 at 100% speed
1 + ROUND[(1 * 50) * ((1 + 0.005 * (2-1) / 35) * (100 / 100 + 1) ^ 2]
1 + ROUND[50 * 0.0287142... * 4]
1 + ROUND[5.742857...]
= 7 deuterium

Fleets of multiple ship types
Cost per ship type = Fuel * (Distance / 35'000) * (% / 100 * ((speed of the slowest ship type) / (Speed of current ship type)) ^ (1 / 2) + 1) ^ 2
Total cost of the fleet = 1 + ROUND(Sum of each ship type's cost)
It is important to note that the costs should not be rounded until the end.

Example:
Fleet of 1 Cruiser, 1 Battleship, and 1 Recycler travelling from 3:22:1 to 2:22:1 at 50% speed
Speeds are at requirement drive levels: Cruiser 27'000, Battleship 22'000, Recycler 3'200
Cost of the Cruiser:
300 * (20'000 / 35'000) * (50 / 100 * ((3'200) / (27'000)) ^ (1 / 2) + 1) ^ 2
= 235.5248256...
Cost of the Battleship:
500 * (20'000 / 35'000) * (50 / 100 * ((3'200) / (20'000)) ^ (1 / 2) + 1) ^ 2
= 411.4285714...
Cost of the Recycler:
300 * (20'000 / 35'000) * (50 / 100 * ((3'200) / (3'200)) ^ (1 / 2) + 1) ^ 2
= 385.7142857...
Total cost of the fleet:
1 + ROUND(235.5248256... + 411.4285714... + 385.7142857...)
= 1034 deuterium

Deuterium Costs for ACS Defends and Expeditions:
Hold costs per hour are 1/10 the of the fuel usage.
Small Cargo- 2 deut per hour
Large Cargo- 5 deut per hour
Light Fighter- 2 deut per hour
Heavy Fighter- 7 deut per hour
Cruiser- 30 deut per hour
Battleship- 50 deut per hour
Colony Ship- 100 deut per hour
Recycler- 30 deut per hour
Espionage Probe- 1/10 deut per hour
Bomber- 100 deut per hour
Destroyer- 100 deut per hour
Deathstar- 1/10 deut per hour
Battlecruiser- 25 deut per hour

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Moons:
Number of ships needed for X% Moonchance:
(100'000 * X) / ((metal + crystal cost of one ship) * 0.3)

Moon Destruction mission:
The percent chance to kill the moon is:
(100 - (Moonsize) ^ (1 / 2)) * (number of death stars) ^ (1 / 2)

The percent chance the attacking fleet is destroyed:
((Moonsize) ^ (1 / 2)) / 2

Sensor Phalanx:
Range of a Sensor Phalanx
(level phalanx) ^ 2 - 1 systems

What a phalanx can see:

If you scan the origin planet:

- All outbound fleets except deployment mission
- Fleets returning from their mission
- All fleets recalled from their mission except deployment

The time displayed will be the total time left in the mission.

If you scan the target planet:
- All inbound fleets

What a phalanx can't see:

If you scan the target planet:

- Fleets recalled from deployment mission
- Fleets heading towards that planet's moon or debris field from elsewhere
- Fleets returning from a mission

If you scan the origin planet:

- Fleets recalled from deployment mission

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Actual Armour, Weapons, and Shielding strengths:
Actual Strength = (Base Strength) * (1 + ((Technology Level) * 0.1))
In battle, hull is used, which is (Structural Integrity) / 10.

Example:
Battlecruiser at level 6 Armour, Weapons, and Shielding Technologies (Base 70'000 structural integrity, 700 attack, and 400 shields)
Hull:
(70'000 / 10) * (1 + ((6) * 0.1))
= 11'200
Weapons:
(700) * (1 + ((6) * 0.1))
= 1'120
Shielding:
(400) * (1 + ((6) * 0.1))
= 640

Chance to fire again from rapidfire:
% Chance to fire again = 100 - 100 / (Rapidfire)

Example:
1 Battlecruiser firing on 1 Battleship (rapidfire vs Battleship is 7)
100 - 100 / 7
= 85.7142857...% chance to fire again that round of combat

More information on rapidfire can be found at Rapidfire.

For more information about combat itself works, see How a fight works.

How are resources captured when you attack a planet:
Please note that you can only capture up to 50% of the overall resources on a planet.

For example, if you attack a planet which has 20'000 metal, 20'000 crystal and 10'000 deuterium, you will get be able to capture a maximum of 25'000 resources overall {(20'000+20'000+10'000)/2}.

Now here is how each resources are captured and its called the "plunder algorithm":
1. Fill up to 1/3 of cargo capacity with metal
2. Fill up to half remaining capacity with crystal
3. The rest will be filled with deuterium
4. If there is still capacity available fill half of it with metal
5. Now fill the rest with crystal

Be wary when attacking planets with more metal than any other resource. Due to how the algorithm works, it takes more cargo capacity than it may seem to capture 50% of the metal. It is of note that SpeedSim correctly predicts the number of cargos for full capture despite this issue.

Example:
Attacking a planet that has 30'000 metal, 20'000 crystal and 10'000 deut with 6 small cargos (30'000 total cargo capacity)
1. 30'000 / 3 = 10'000 metal
2. 20'000 / 2 = 10'000 crystal
3. We have 10'000 capacity left, but we can only capture up to 5'000 deuterium
4. 5'000 / 2 = 2'500 more metal, for a total of 12'500 metal
5. We have already captured half of the crystal on the planet.
So in this example we have captured 12'500 metal, 10'000 crystal, and 5'000 deuterium.

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Speed universes
Speed universes decrease the time it takes for fleets to fly and projects to complete, and they increase the mine production. To calculate for these unis, multiply or divide the final result of the above formulas by the speed factor of the universe.

Formulas which are multiplied:
-Metal Mine, Crystal Mine, and Deuterium Synthesizer production
-Fusion Reactor deuterium consumption

Formulas which are divided:
-Build times of Buildings, Ships, and Defense
-Research times
-Flight times
-Jumpgate recharge times (normal is 1 hour)
-ACS Defend and Expedition hold times
-Interplanetary Missile flight times

-Minimum time in vacation mode is set to 24 hours in all speed universes.

Speed universes in OGame.org:
-Universe 30, x2
-Universe 35, x5
-Universe 40, x2 (also 40% of destroyed ships go into the DF instead of the normal 30%)
-Universe 42, x2 (Redesign universe)
-Universe Electra, x4 (Redesign universe)