This section summarizes the statistics that determine success in combat, then details how to use them.
An attack roll represents your attempt to strike your opponent on your turn in a round. When you make an attack roll, you roll a d20 and add your attack bonus. (Other modifiers may also apply to this roll.) If your result equals or beats the target's Armor Class, you hit and deal damage.
A natural 1 (the d20 comes up 1) on an attack roll is always a miss. A natural 20 (the d20 comes up 20) is always a hit. A natural 20 is also a threat—a possible critical hit.
Your attack bonus with a melee weapon is the following:
Base attack bonus + Strength modifier + size modifier
With a ranged weapon, your attack bonus is the following:
Base attack bonus + Dexterity modifier + size modifier + range penalty
Your Armor Class (AC) represents how hard it is for opponents to land a solid, damaging blow on you. It's the attack roll result that an opponent needs to achieve to hit you. Your AC is equal to the following:
10 + armor bonus + shield bonus + Dexterity modifier + other modifiers
Note that armor limits your Dexterity bonus, so if you're wearing armor, you might not be able to apply your whole Dexterity bonus to your AC (see Armor and Shields).
Sometimes you can't use your Dexterity bonus (if you have one). If you can't react to a blow, you can't use your Dexterity bonus to AC. If you don't have a Dexterity bonus (or have a Dexterity penalty), your AC does not change.
Many other factors modify your AC.
Enhancement bonuses apply to your armor to increase the armor bonus it provides.
Magical deflection effects ward off attacks and improve your AC.
If your race has a tough hide, scales, or thick skin you receive a bonus to your AC.
Dodge bonuses represent actively avoiding blows. Any situation that denies you your Dexterity bonus also denies you dodge bonuses. (Wearing armor, however, does not limit these bonuses the way it limits a Dexterity bonus to AC.) Unlike most sorts of bonuses, dodge bonuses stack with each other.
You receive a bonus or penalty to your AC based on your size. See the Size Modifiers Table.
Some attacks completely disregard armor, including shields and natural armor—the aggressor need only touch a foe for such an attack to take full effect. In these cases, the attacker makes a touch attack roll (either ranged or melee). When you are the target of a touch attack, your AC doesn't include any armor bonus, shield bonus, or natural armor bonus. All other modifiers, such as your size modifier, Dexterity modifier, and deflection bonus (if any) apply normally.
Some creatures have the ability to make incorporeal touch attacks. These attacks bypass solid objects, such as armor and shields, by passing through them. Incorporeal touch attacks work similarly to normal touch attacks except that they also ignore cover bonuses. Incorporeal touch attacks do not ignore armor bonuses granted by force effects, such as mage armor and bracers of armor.
If your attack succeeds, you deal damage. Damage reduces a target's current hit points. The type of weapon used determines the amount of damage you deal.
If penalties reduce the damage result to less than 1, a hit still deals 1 point of nonlethal damage.
When you hit with a melee or thrown weapon, including a sling, add your Strength modifier to the damage result. A Strength penalty, but not a bonus, applies on damage rolls made with a bow that is not a composite bow.
When you deal damage with a weapon in your off hand, you add only 1/2 your Strength bonus. If you have a Strength penalty, the entire penalty applies.
When you deal damage with a weapon that you are wielding two-handed, you add 1-1/2 times your Strength bonus (Strength penalties are not multiplied). You don't get this higher Strength bonus, however, when using a light weapon with two hands.
Sometimes you multiply damage by some factor, such as on a critical hit. Roll the damage (with all modifiers) multiple times and total the results.
When you multiply damage more than once, each multiplier works off the original, unmultiplied damage. So if you are asked to double the damage twice, the end result is three times the normal damage.
Extra damage dice over and above a weapon's normal damage are never multiplied (such as magical energy damage or sneak attack damage).
Certain creatures and magical effects can cause temporary or permanent ability damage (a reduction to an ability score).
When your hit point total reaches 0, you're disabled. When it reaches –1, you're dying. When it gets to a negative amount equal to your Constitution score, you're dead. See Injury and Death, for more information.
Your speed tells you how far you can move in a round and still do something, such as attack or cast a spell. Your speed depends mostly on your size and your armor.
Dwarves, gnomes, and halflings have a speed of 20 feet (4 squares), or 15 feet (3 squares) when wearing medium or heavy armor (except for dwarves, who move 20 feet in any armor).
Humans, elves, half-elves, half-orcs, and most humanoid monsters have a speed of 30 feet (6 squares), or 20 feet (4 squares) in medium or heavy armor.
If you use two move actions in a round (sometimes called a "double move" action), you can move up to double your speed. If you spend the entire round running, you can move up to quadruple your speed (or triple if you are in heavy armor).
Generally, when you are subject to an unusual or magical attack, you get a saving throw to avoid or reduce the effect. Like an attack roll, a saving throw is a d20 roll plus a bonus based on your class and level, and an associated ability score. Your saving throw modifier is:
Base save bonus + ability modifier
These saves measure your ability to stand up to physical punishment or attacks against your vitality and health. Apply your Constitution modifier to your Fortitude saving throws.
These saves test your ability to dodge area attacks and unexpected situations. Apply your Dexterity modifier to your Reflex saving throws.
These saves reflect your resistance to mental influence as well as many magical effects. Apply your Wisdom modifier to your Will saving throws.
The DC for a save is determined by the attack itself.
A natural 1 (the d20 comes up 1) on a saving throw is always a failure (and may cause damage to exposed items; see Items Surviving after a Saving Throw). A natural 20 (the d20 comes up 20) is always a success.