Worked example
Two parts stacked, 20 ±0.1 and 30 ±0.2, sit in a housing 49.5 ±0.1. The gap is 20 + 30 − 49.5 = 0.5. Worst case: the half-tolerances add, 0.1 + 0.2 + 0.1 = 0.4, so the gap is between 0.1 and 0.9 – it never closes. RSS: √(0.1² + 0.2² + 0.1²) = 0.245, so the gap is 0.255 to 0.745 for most assemblies. These are the values preset above.
Worst case or RSS?
- Worst case for safety-critical or low-volume assemblies, and whenever a failure must be impossible rather than rare.
- RSS for high volumes with processes that are centred and under control (see the Cpk calculator): the tolerances can be wider for the same assembly quality. Typically a tolerance of ±3σ per dimension is assumed; if your parts are not centred, RSS understates the risk.
- Non-linear stacks, such as angles or parts that tilt, need a model of their own; this calculator handles straight, one-dimensional chains.
Related
For the limits of one shaft in one hole, see the fit and clearance calculator.
Frequently asked questions
How do I calculate a tolerance stack-up?
Add the dimensions with their direction (+ or −) to get the nominal gap. For worst case add all the half-tolerances; for RSS take the square root of the sum of their squares. 20 ±0.1, 30 ±0.2 and 49.5 ±0.1 (subtracting) give a gap of 0.5, worst case 0.1 to 0.9, RSS 0.255 to 0.745.
What is the difference between worst case and RSS?
Worst case assumes every part is at its limit in the worst direction at once, so the result is always safe and the tolerances end up tight. RSS assumes independent, centred deviations that partly cancel, which is realistic for many parts and processes under control.
When should I use RSS?
For high volumes with centred, capable processes and several contributors. For safety-critical or small-batch assemblies, use worst case.
Does this handle angles or tilting parts?
No. It handles straight, one-dimensional chains. Angles, tilt and three-dimensional stacks need a model of their own.
More free machinist calculators
- Inch to mm – Convert inches to millimetres and back, fractions like 1 3/8 included. Exact factor 25.4, with a chart of every 1/64 inch.
- RPM and feed – Calculate spindle RPM from surface speed and diameter, surface speed from RPM, and feed rate from chip load – metric and imperial, with formulas.
- Taper – Taper ratio, half angle and taper per foot from the large and small diameter and the length, or the small diameter from the angle.
- Bolt circle – X and Y coordinates of evenly spaced holes on a bolt circle, with the hole spacing, start angle and centre offset. Copy the table into your program.
- Sine bar – Gauge block height for a sine bar angle, or the angle from a known stack, for 5 in, 10 in, 100 mm, 200 mm or any other bar length.
- Metal removal rate – Metal removal rate in cm³/min or in³/min from depth, width and feed – milling and turning, metric and imperial, with the formulas.
- Drill point depth – Length of a drill's point cone from diameter and point angle, and the total depth needed for a full-diameter hole to depth.
- Right triangle – Hypotenuse and angles from two legs, or the legs from the hypotenuse and an angle – for chamfers, dovetails, tapers and hole positions.
- Machining time – Cutting time from length, feed and spindle speed – turning with feed per revolution, milling with feed rate and number of passes.
- Decimal to fraction – Turn a decimal inch or a millimetre value into the nearest fraction – 8ths to 128ths – with the error in millimetres.
- Degrees to DMS – Convert decimal degrees to degrees, minutes and seconds and back, with the angle in radians.
- SFM to m/min – Convert surface feet per minute to metres per minute and back, and inches per minute to mm per minute, with the exact factors.
- TPI to pitch – Convert a thread pitch in millimetres to threads per inch (TPI) and back, for matching metric and inch threads.
- Cpk calculator – Paste measurements from Excel, enter USL and LSL and get Cp, Cpk, Pp and Ppk. Says plainly when 25 values are too few for an index.
- Fit clearance – Enter hole and shaft limits and get minimum and maximum clearance and the kind of fit – clearance, transition or interference.
- Chip thinning – Feed per tooth to program when the radial width of cut is below half the cutter diameter, so the real chip thickness stays right.
- Ball-nose stepover – Scallop height left by a ball-nose cutter from the stepover, or the stepover for a wanted scallop height, on a flat surface.
- Surface finish – Theoretical Rt and estimated Ra of a turned surface from the feed per revolution and the tool nose radius.
- Torque and power – Torque from power and speed in newton-metres or pound-feet, and power from torque and speed. The formulas with worked examples.
- Spur gear – Pitch and outside diameter, centre distance, ratio and circular pitch of a pair of external spur gears from the module and the tooth numbers.
Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.