Writing a story in which a human is trapped on an alien planet with an average temp of 6 Celsius, and I want to have the atmosphere be too rich in oxygen, but not to the point where an air tank is necessary. What combination of pressure and oxygen would make a human just functional?
Alas, I couldn't find exact details of what percentage of O2 would be the limit; The best I could find for details is the chart below. I did, however, find details on what overdosing of oxygen can do.
Apparently, too much oxygen intake can lead to issues with how cells can function. It leads to overproduction of something called ROS, which affects how cells can intake nutrients and can damage tissues. Particularly at risk are the lungs, heart, and brain.
For more details, I've provided some links below the charts. Hope this helps.
It depends on the atmospheric pressure.
This chart from NASA shows the relationship between O2 concentration, atmospheric pressure, and how comfortable a human will be breathing that atmosphere. You could actually survive in atmosphere with 100% oxygen, just at a much lower pressure than on Earth. On this chart you can see the border for survivable O2 toxicity in a 100% O2 environment is ~8psia, or just above half Earth's atmospheric pressure.
With a pressure this low and with no gases besides Oxygen this planet would indeed be significantly colder than Earth, I would suspect even colder than an average temp of 6C. A thin atmosphere combined with a lack of greenhouse gases leads to a low surface temperature as heat from the sun is quickly lost.
To bring your planet's temperature up it should probably orbit closely to a hot star and have a very low surface albedo (a very black planet) and/or trade some oxygen for a strong greenhouse gas like water (unlikely if your planet is so cold), CO2, or methane. Closely orbiting a hot star with a thin atmosphere would introduce more problems like solar radiation and a large temperature difference between day and night. Additionally you should not try to start a fire in an Oxygen/Methane atmosphere. Or in any high Oxygen environment for that matter.
I don't have the precise math with me now, but there are some models out there which can estimate stuff like this. I can edit this later with more specific numbers if you'd like.
EDIT: A planet just like earth but with a 100% Oxygen atmosphere would likely have an average surface temperate of about -20C.
This page describes conditions within a space-craft, however the same concepts apply.
Other answers have addressed the issue of O2 partial-pressure that humans can tolerate. I want to point out other potential issues.
Oxygen is very reactive. The higher the oxygen content, the easier it is for a fire to start / spread. And anything that can oxidize will do so more quickly when exposed to the atmosphere.
A 100% oxygen atmosphere is not very plausible, AFAIK. I don't think any naturally-evolving life could maintain it, since it would always be reacting with things to produce other gases (e.g. CO2).
CO2 partial-pressure is also a big deal for humans. If it's too high, CO2 won't diffuse out of the bloodstream back into the air in the lungs, leading to changes in blood acidity as more CO2 builds up. CO2 toxicity is a thing. It's nowhere near as bad as carbon monoxide, and I haven't yet found a reliable number on CO2 partial pressure that would be dangerous. What I've found so far suggests that increasing oxygen partial-pressure wouldn't compensate for increased CO2 partial-pressure very much or at all.
Interesting options for your atmosphere:
Total pressure ~= Earth sea level. 60% O2 (upper limit for indefinite human survival), rest a mix of Nitrogen and other gases with a biome similar to earth. Just really aggressive plants or something.
Total pressure = ~twice Earth. Similar ratios to Earth for other gases (unless that makes too high a CO2 partial pressure).
Total pressure = ~twice Earth. 25% O2 (partial pressure more than twice Earth). Other gases very different from Earth. Maybe inert gases like Argon and/or Helium making up a large fraction? A heavy planet could hold its helium better than Earth, maybe enough to stop it from escaping into space at the top of the atmosphere? I haven't run the numbers, but maybe helium is still implausible.
Make sure your atmosphere isn't combustible, though, because there's always lightning or other sources of fire. If the atmosphere could ignite / detonate, it would already have done so.
I don't think you should consider less than Earth sea level total pressure, since a dangerously-high O2 partial pressure for humans would make it even more than 60% of the total gas, and then you'd need a mechanism to explain that.
Humans routinely breath 100% O2 without issue. Divers, astronauts and patients routinely breath 100% Oxygen. There are some dangers of High Oxygen concentration such as absorption atelectasis(collapse of the small air sacks in the lungs) and the suppression the Hypoxic respiratory drive in some COPD patients whose chronic CO2 retention has burnt out their normal CO2-realted drive, causing them to stop breathing. Most dangers, though are related to the high partial pressure of Oxygen.
Science uses the measure of partial pressure of O2 to talk about the Oxygen concentration and pressure. Quickly stated, each gas in a mixture exerts a pressure equal to their percentage in the mixture. So at sea level, atmospheric pressure is 14.70 PSI. O2, being about 21% of the atmosphere, exerts a pressure equal to .21*14.7 =3.08 PSI.
According to Wikipedia, The minimum and maximum Partial Pressures of O2 for human life are 2.3 PSI and 14.5 PSI.
The minimum safe partial pressure of oxygen in a breathing gas is commonly held to be 16 kPa (0.16 bar).
The maximum safe ppO2 in a breathing gas depends on exposure time ... It is typically between 100 kPa (1 bar) and 160 kPa (1.6 bar)
It is primarily about partial pressure rather than concentration*, so pretty much any concentration can be just fine if the pressure is appropriate.
The US EMU spacesuit uses 100% oxygen at 29.6 kPa (~4.3 psi) - https://www.nasa.gov/pdf/188963main_Extravehicular_Mobility_Unit.pdf
The acute nervous-system oxygen toxicity (seizures etc.) that has killed a lot of scuba divers happens well above 1 bar / 15 psi; you wouldn't get this at sea level pressure even with pure oxygen.
In between, you get lesser effects which increase with time - Wikipedia claims below 0.5 bar is fine indefinitely, for lung effects at least, apparently based on a 1987 study.
*At very low pressures total pressure matters as well - 3 psi 100% O2 gives you significantly less oxygen than sea level air, even though the partial pressure is the same, because of vapor pressure of water (and presence of CO2 too, I think) in the lung.