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You probably should just use the spell text: Source
PRPG Core Rulebook pg. 301
Casting
Casting Time 1 standard action
Components V, S, M/DF (an eyelash encased in gum arabic)
Effect
Range personal or touch
Target you or a creature or object weighing no more than 100 lbs./level
Duration 1 min./level (D)
Saving Throw Will negates (harmless) or Will negates (harmless, object); Spell Resistance yes (harmless) or yes (harmless, object)
Description
The creature or object touched becomes invisible. If the recipient is a creature carrying gear, that vanishes, too. If you cast the spell on someone else, neither you nor your allies can see the subject, unless you can normally see invisible things or you employ magic to do so.
Items dropped or put down by an invisible creature become visible; items picked up disappear if tucked into the clothing or pouches worn by the creature. Light, however, never becomes invisible, although a source of light can become so (thus, the effect is that of a light with no visible source). Any part of an item that the subject carries but that extends more than 10 feet from it becomes visible.
Of course, the subject is not magically silenced, and certain other conditions can render the recipient detectable (such as swimming in water or stepping in a puddle). If a check is required, a stationary invisible creature has a +40 bonus on its Stealth checks. This bonus is reduced to +20 if the creature is moving. The spell ends if the subject attacks any creature. For purposes of this spell, an attack includes any spell targeting a foe or whose area or effect includes a foe. Exactly who is a foe depends on the invisible character's perceptions. Actions directed at unattended objects do not break the spell. Causing harm indirectly is not an attack. Thus, an invisible being can open doors, talk, eat, climb stairs, summon monsters and have them attack, cut the ropes holding a rope bridge while enemies are on the bridge, remotely trigger traps, open a portcullis to release attack dogs, and so forth. If the subject attacks directly, however, it immediately becomes visible along with all its gear. Spells such as bless that specifically affect allies but not foes are not attacks for this purpose, even when they include foes in their area.
Invisibility can be made permanent (on objects only) with a permanency spell.Keep in mind that you are looking at two separate things here:
- Adjustments to your Stealth check, and
- Adjustments to your 'Invisible' adjustment to your Stealth check.
Finally, sneaking around to attack someone by yourself is essentially suicide: Encounters are generally balanced around an entire group participating...
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You are misreading the table for invisibility. It says the perception check to spot an invisible opponent is 20, but this is then modified by various things, one of which is -5 for them moving at half speed. That's for a situation where the invisible person is not using stealth.
e.g. Bob the fighter with zero stealth skill is invisible. Difficulty to perceive him is 20. Bob starts moving at 1/2 speed (he got hit by a Slow spell or something) Difficulty to perceive him is now 15 (20-5) because he is making noise, kicking up dust or moving the furniture as he goes past.
BUT If you are actively trying to be stealthy (reducing noise etc) you make a Stealth check +20 -0 (because there is no penalty for stealthing at half speed), and that becomes the target for the opponent's perception check.
e.g. Fred the rogue has a stealth skill of +10 and is walking next to Bob. He rolls a 15 on his stealth skill. That means the difficulty to perceive him is now 45 (10+15+20) i.e. vastly harder because he is using his skill to stay silent and not disurb anything as he passes.
Invisible rules: reference:
https://aonprd.com/Rules.aspx?ID=431
Moving at half speed -5
Moving at full speed -10
Running or charging -20
You stopped listing them two lines too early...
"Using Stealth Stealth Check +20"So if you're stealthing it's your stealth check +20.
The 6th line in the chart is Using Stealth and it says Stealth Check +20. What that means you use your normal stealth roll with any penalties (including those listed under stealth for movement) with a +20 and use that for the DC of the perception roll instead of using the modifiers on the chart.
Stealth is an opposed roll vs perception not a modifier to your perception. That chart is for modifiers to the perception roll.