How sensitive exactly is called equilibrium climate sensitivity (ECS). Climatologists compute it using global climate models and different climatology groups have different models, so they produce different numbers. Unfortunately the span is wide and has been getting wider with time as the simulations become more detailed, so confidence in this value has been falling. This isn't meant to happen and we're rarely directly told it is, actually we're told the opposite (that there is consensus on everything).
IPCC 2013 AR5: "No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence".
The most recent IPCC reports try to solve this by de-weighting the models that compute a high ECS i.e. a highly sensitive climate. They do this because they know the models must be wrong, as they conflict with observational data. The climate can't actually be all that sensitive to CO2 relative to what some climatologists try to claim. Unfortunately most climatological research does not do this and assumes all models are equally valid, so justs averages all of them. It's clearly not valid when error bars are so wide.
Also, this situation leads to the obvious question of why not simply compute ECS from observed data to begin with? Unfortunate answer: because if you do, you get a very low value indeed (see the work of Lewis). With ECS values that low CO2 stops being a significant environmental problem and is probably less important than other environmental problems like e.g. clean rivers, biodiversity. Climatologists don't like to do this and prefer to continue deriving values from models, even though they know that at least some of them cannot be correct.
tl;dr - what you state as fact is actually one of the most bitterly argued and controversial aspects of climate science. They have a way to express it numerically but nobody can agree what the right number is.
How sensitive exactly is called equilibrium climate sensitivity (ECS). Climatologists compute it using global climate models and different climatology groups have different models, so they produce different numbers. Unfortunately the span is wide and has been getting wider with time as the simulations become more detailed, so confidence in this value has been falling. This isn't meant to happen and we're rarely directly told it is, actually we're told the opposite (that there is consensus on everything).
IPCC 2013 AR5: "No best estimate for equilibrium climate sensitivity can now be given because of a lack of agreement on values across assessed lines of evidence".
The most recent IPCC reports try to solve this by de-weighting the models that compute a high ECS i.e. a highly sensitive climate. They do this because they know the models must be wrong, as they conflict with observational data. The climate can't actually be all that sensitive to CO2 relative to what some climatologists try to claim. Unfortunately most climatological research does not do this and assumes all models are equally valid, so justs averages all of them. It's clearly not valid when error bars are so wide.
Also, this situation leads to the obvious question of why not simply compute ECS from observed data to begin with? Unfortunate answer: because if you do, you get a very low value indeed (see the work of Lewis). With ECS values that low CO2 stops being a significant environmental problem and is probably less important than other environmental problems like e.g. clean rivers, biodiversity. Climatologists don't like to do this and prefer to continue deriving values from models, even though they know that at least some of them cannot be correct.
tl;dr - what you state as fact is actually one of the most bitterly argued and controversial aspects of climate science. They have a way to express it numerically but nobody can agree what the right number is.