Why frame reach and stack are not enough
Reach and stack replaced seat tube length as the way frames are compared because they describe one fixed relationship: the horizontal and vertical distance from the bottom bracket to the top of the head tube. Two frames with the same reach and stack put the top of the head tube in the same place, regardless of how the tubes get there.
The trouble is that nobody holds the top of the head tube. Between there and your hands sit the headset top cap, some number of spacers, and a stem with a length and an angle, and those parts move the bar by more than the differences between frame sizes typically do. A 100 mm stem contributes roughly a hundred millimetres of forward position, which is larger than the reach gap between two consecutive frame sizes.
So the comparison that answers the question people are actually asking is at the bar clamp, not at the head tube. That is what this page computes, and it is why the interesting number is usually the difference between two setups rather than either absolute figure.
The geometry, spelled out
Take the bottom bracket as the origin. The top of the head tube is at the frame reach forward and the frame stack up. From there the steerer runs upward and backward at the head tube angle measured from horizontal, so travelling a distance d along it adds d × sin(angle) of height and subtracts d × cos(angle) of reach. On a 73 degree head angle, 40 mm of spacer stack gains 38.3 mm of height and gives up 11.7 mm of reach. That trade is the reason a rider who raises the bars usually finds them closer as well as taller.
The distance d used here is the spacers and top cap plus half the stem clamp height, because the stem pivots about the middle of its clamp rather than its bottom edge.
The stem then runs out from the steerer at an angle perpendicular to it when marked zero. A steerer at 73 degrees means a zero degree stem points 17 degrees above horizontal, and a stem marked minus six sits at 11 degrees above horizontal. That is a point riders frequently get backwards: a negative stem on a road bike still rises, because the head angle is doing more than the stem marking is.
Worked all the way through, a 385 reach and 565 stack frame at 73 degrees, with 20 mm of spacers, a 40 mm clamp and a 100 mm stem at minus six, puts the bar clamp at 471.5 mm of reach and 622.3 mm of stack. Flip the same stem to plus six and it moves to 465.4 and 642.3, which is 20 mm of height bought for 6 mm of reach.
Which adjustment does what
| Change | Reach | Stack | Also changes |
|---|---|---|---|
| Add 10 mm of spacers | −2.9 mm | +9.6 mm | Nothing else, within the steerer available |
| Stem 10 mm longer | +9.8 mm | +1.9 mm | Steering feel becomes slower and more damped |
| Flip a 6 degree stem up | −6.1 mm | +20.0 mm | Nothing, and it costs nothing |
| Move the saddle back 10 mm | Effectively +10 mm | No change | Knee position over the pedal, which is a separate question |
Figures shown are for a 73 degree head angle and a 100 mm stem. Two things follow. The first is that spacers are a height tool with a small reach side effect, and stem length is a reach tool with a small height side effect, so the two together can reach almost any bar position within a sensible range. The second is that flipping a stem is the largest free adjustment available on most bikes, and it is worth trying before buying anything.
Saddle position is deliberately outside this calculation. Moving the saddle changes the distance to the bars, but it also changes where you sit relative to the pedals, which is determined by entirely different considerations. Using saddle fore-aft to fix reach is the most common way a fit goes wrong.
How much difference is a real difference
Five millimetres at the bar is within the noise of how you set your saddle up on a given day and how much padding is in your bar tape. Ten is noticeable to most riders on a long ride. Twenty is a different bike, and it is beyond what a stem swap fixes gracefully, because a stem long enough or short enough to close a 20 mm gap starts to change how the bike steers.
Stem length has a handling consequence that reach numbers do not capture. A short stem makes steering feel quick and slightly nervous; a long one makes it feel slow and stable. Beyond roughly 60 to 130 mm on a road bike most riders notice the change in behaviour more than the change in position, which is a good argument for picking a frame whose reach lands near the stem length you like rather than correcting a large gap with hardware.
What the numbers still do not tell you
Bar clamp position is not hand position. Handlebars have their own reach and drop, the levers can be rotated and shifted around the curve, and two bars clamped in identical places can put the hoods thirty millimetres apart and the drops further still. If you are comparing complete bikes rather than frames, the bar and lever geometry has to be added or the comparison is incomplete.
And geometry says nothing about whether a position suits a body. Flexibility, hip structure, injury history and how long you intend to stay in the position all matter more than any millimetre here, and none of them is a number a frame carries. Persistent numbness, pain or loss of sensation is a reason to see a fitter or a clinician, not a reason to move a spacer. For the training side of what the position is for, the power zones calculator and the climb power calculator deal with what the bike is asked to do; for keeping the parts you are adjusting in good order, the bike maintenance guide covers the routine, and the bike and scooter safety guide covers riding around traffic.
Questions people ask
What are reach and stack, exactly?
Reach is the horizontal distance from the bottom bracket centre to the centre of the top of the head tube, and stack is the vertical distance between the same two points. They were adopted because they describe frame size in a way that does not depend on tube angles or on whether the top tube slopes, which the older seat tube and top tube measurements did. Two frames with matching reach and stack put the top of the steerer in the same place, whatever their other dimensions. What they do not describe is where the handlebar goes, because that depends on spacers, stem length and stem angle, which is what this calculator adds.
Why does adding spacers pull the bars closer as well as higher?
Because the steerer tube is not vertical. It leans backward at the head tube angle, typically 71 to 74 degrees from horizontal on a road bike, so moving up along it also moves backward. At 73 degrees, every 10 mm of spacer gains about 9.6 mm of height and gives up about 2.9 mm of reach. Riders who raise the bars to relieve back or neck discomfort often find the position now feels cramped as well as taller, and the usual correction is a slightly longer stem to give the reach back. Slacker head angles, common on mountain bikes, make the effect larger.
Is a negative stem angle pointing down?
Relative to the steerer, yes; relative to the ground, usually not. Stem angles are marked relative to perpendicular to the steerer, and since a road head tube leans back at around 73 degrees, a stem marked zero already points about 17 degrees above horizontal. A minus six stem therefore sits at about 11 degrees above horizontal and still rises. To get a bar clamp below the top of the head tube you would need a stem angle steeper than the complement of the head angle, which is rare on road bikes and more common on time trial setups. Flipping a stem changes the sign of the marked angle, which on a 6 degree stem is worth about 20 mm of height.
Can I use this to pick a frame size?
It can tell you whether two frames can be made to put your hands in the same place, which is a genuinely useful part of that decision but not the whole of it. What it cannot tell you is which position you should be in, which depends on your body and your riding rather than on arithmetic. The practical method is to start from a bike you already ride comfortably, compute its bar reach and stack here, and then check what stem and spacer combination a candidate frame needs to reproduce them. If the answer is a stem length inside the normal range and a spacer stack the steerer can accommodate, the frame can work. If it needs a 140 mm stem or negative spacers, it cannot.
Where does saddle position fit into this?
It is a separate axis and mixing it in is the classic fitting error. Saddle height and fore-aft position are set by the relationship between you and the pedals, and moving the saddle backward to reach a bar that is too close changes your position over the cranks in a way that affects power and knee loading. The reach problem is a stem and spacer problem. Once the saddle is where it needs to be relative to the bottom bracket, the bar position is what this calculator addresses, and the two conversations should stay separate even though both change the distance between saddle and bars.