A matching bolt and nut convert relative rotation into axial motion through their helical threads. For the single-start model here, one revolution advances the nut by one pitch. The calculator keeps this motion explicit and shows the difference between pitch, selected turns and helix angle. It does not calculate a bolted joint’s strength or tightening torque.
Powered linear positioning
A screw drive converts motor rotation into linear travel. The bolt-and-nut model below explains the pitch-to-travel relationship, but it does not calculate the force or torque needed by a loaded powered drive.
For a separate powered positioning application, compare the required force, stroke and mounting space with the FIRGELLI linear actuator range. The actuator force calculator covers supported mounting arrangements; the replacement finder helps compare an existing actuator with available options.
Common Screw Bolt and Nut Interactive Calculator
Watch a hex nut rotate and move along a stationary single-start bolt. Thread pitch determines axial advance per revolution; the selected number of turns determines total travel. Diameter changes the bolt proportions and the helix angle evaluated at that diameter.
Equation Used
- One thread start and a rigid matching nut; no backlash or deformation.
- Nut rotation relative to the stationary bolt produces axial travel equal to turns times pitch.
- Animation advances through the selected turns and reverses without implying a clamped joint.
- Thread depth, nut height, hex dimensions and shaft length are drawing proportions, not manufacturing dimensions.
- No material or load model; required engagement, preload and torque are not determined.
Single-start free-travel model. Helix angle is evaluated at nominal diameter d. Illustrative thread/hex dimensions are not a standard fastener specification. No torque, preload, strength or minimum engagement recommendation.
Rotation and axial advance
The bolt remains stationary while the hex nut turns and moves along its axis. The colored corner mark makes nut rotation visible. Every full relative revolution produces one pitch of travel. Playback moves from the starting position through the selected turns, then reverses along the same thread.
The bolt length adapts to show the complete travel while keeping the nut engaged in the illustration. Its external thread follows a continuous helix. The nut conceals the portion of the bolt inside it. Thread depth and hex proportions are simplified for explanation, not taken from a fastener standard.
The lower diagram unwraps one turn of a helix on the entered diameter into a right triangle. Its horizontal side is πd and its rise is the pitch. This links the angle result to the actual geometry used by the calculator.
What the model explains
Use the calculator to compare the free axial movement produced by turning a matching single-start nut. A larger pitch produces more movement per turn. More turns produce proportionally more total travel. Changing diameter alone does not change travel per turn.
A real bolted joint behaves differently after its bearing surfaces seat: further tightening deforms the joint and stretches the bolt. The free-travel animation has no clamped members and does not predict that loaded behavior.
Pitch, turns and helix angle
For one thread start, lead equals pitch p. N relative revolutions therefore give axial travel x = Np. The number of turns required for one millimeter is 1/p when pitch is expressed in millimeters per turn.
Unwrapping a helix on diameter d gives circumference πd and rise p. The angle on that cylinder is atan[p/(πd)]. Here d is the entered nominal diameter. Do not treat that result as the pitch-diameter lead angle of a specified ISO thread; the required thread profile and pitch diameter are not supplied.
No minimum engagement length follows from these three inputs. Engagement strength depends on the thread system, material properties, tolerances and applied loading, so the calculator does not recommend a fixed multiple of diameter.
Worked motion example
With diameter 10 mm, pitch 1.5 mm and one turn, free axial travel is 1.5 mm. The nominal circumference is 31.42 mm and the helix angle on that diameter is 2.73°. One millimeter of travel requires 0.667 turn.
Selecting four turns gives 6 mm of travel without changing the helix angle. Changing pitch to 3 mm gives 12 mm for the same four turns and a nominal-diameter helix angle of 5.45°. Changing diameter alone changes the circumference and angle, while leaving travel at Np.
Where this geometric model stops
A coarser single-start pitch advances farther per turn. That statement does not, by itself, establish strength, self-locking, tightening efficiency or load capacity. Those require additional thread and joint information.
The sliders allow broad geometric comparisons, including combinations that are not standard commercial fastener sizes. They do not certify that a particular thread can be manufactured, assembled or used at a given load.
Bolt-and-nut motion questions
Does one turn always move the nut by one pitch?
It does in this single-start, free-travel model. For a multiple-start screw, travel per turn is the lead, equal to pitch multiplied by the number of starts.
Why does diameter not change axial travel?
The thread pitch fixes axial movement per relative revolution. Diameter affects the helix angle, but x = Np has no diameter term.
Why does the animation reverse?
It replays the selected travel without jumping the nut back to its starting point. Reversal undoes the relative rotation and returns along the same helix.
Can I use this to choose tightening torque or engagement length?
No. The model has no material, load, friction, fastener-class or joint-stiffness inputs. Use the appropriate fastener design and assembly specification for those decisions.
Why is the angle labeled at d?
The formula uses the entered nominal diameter. It is not a calculated pitch diameter for a particular thread profile.
References
Thomson, Lead vs. Pitch explains that single-start lead equals pitch and distinguishes multi-start screws. The motion model applies that relationship to relative nut rotation.
NASA Reference Publication 1228, Fastener Design Manual addresses the wider fastener-design topics that this geometric model does not attempt to size.
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