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3D Printing Math Center

Filament, spool budgets, layers, geometry, measured calibration and print planning. 50 tools with purposes, formulas and worked examples.

Simple mode uses starting defaults for extra scenario controls. Advanced exposes those controls where available. Change an entry, then press Calculate.

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Formula, calculation steps & example

All 50 tools: purposes and formulas

Filament cross-sectional area — Filament cross-sectional area using your entered measurements and assumptions.
Result = ((π × (A ^ 2)) ÷ 4); A = Measured filament diameter mm
Filament volume from length — Filament volume from length using your entered measurements and assumptions.
Result = (((π × (A ^ 2)) ÷ 4) × B); A = Diameter mm, B = Filament length meters
Filament mass from length and density — Filament mass from length and density using your entered measurements and assumptions.
Result = ((((π × (A ^ 2)) ÷ 4) × B) × C); A = Diameter mm, B = Length meters, C = Density g/cm³
Filament length from mass — Filament length from mass using your entered measurements and assumptions.
Result = ((A ÷ B) ÷ ((π × (C ^ 2)) ÷ 4)); A = Filament mass g, B = Density g/cm³, C = Diameter mm
Net filament from spool weighing — Net filament from spool weighing using your entered measurements and assumptions.
Result = (A - B); A = Gross spool mass g, B = Empty spool mass g
Whole prints remaining on spool — Whole prints remaining on spool using your entered measurements and assumptions.
Result = floor((A ÷ B)); A = Available filament g, B = Estimated print mass g
Filament price per gram — Filament price per gram using your entered measurements and assumptions.
Result = (A ÷ B); A = Spool price, B = Net filament mass g
Print filament cost — Print filament cost using your entered measurements and assumptions.
Result = (A × B); A = Print filament mass g, B = Price per gram
Support material share — Support material share using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Support mass g, B = Total print mass g
Purge material share — Purge material share using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Purge mass g, B = Total consumed mass g
Uniform layer count — Uniform layer count using your entered measurements and assumptions.
Result = ceil((A ÷ B)); A = Part height mm, B = Layer height mm
Layers with different first layer — Layers with different first layer using your entered measurements and assumptions.
Result = (ceil(((A - B) ÷ C)) + 1); A = Part height mm, B = First layer height mm, C = Later layer height mm
Nominal wall path thickness — Nominal wall path thickness using your entered measurements and assumptions.
Result = (A × B); A = Path line width mm, B = Perimeter count
Top solid layer thickness — Top solid layer thickness using your entered measurements and assumptions.
Result = (A × B); A = Layer height mm, B = Top layer count
Bottom solid layer thickness — Bottom solid layer thickness using your entered measurements and assumptions.
Result = (A × B); A = Layer height mm, B = Bottom layer count
Rectangular extrusion path volume — Rectangular extrusion path volume using your entered measurements and assumptions.
Result = ((A × B) × C); A = Line width mm, B = Layer height mm, C = Path length mm
Rectangular volumetric extrusion rate — Rectangular volumetric extrusion rate using your entered measurements and assumptions.
Result = ((A × B) × C); A = Line width mm, B = Layer height mm, C = Travel speed mm/s
Constant-speed extrusion path time — Constant-speed extrusion path time using your entered measurements and assumptions.
Result = (A ÷ B); A = Path length mm, B = Travel speed mm/s
Filament length for rectangular path — Filament length for rectangular path using your entered measurements and assumptions.
Result = (A ÷ ((π × (B ^ 2)) ÷ 4)); A = Path volume mm³, B = Filament diameter mm
Line width relative to nozzle diameter — Line width relative to nozzle diameter using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Line width mm, B = Nozzle diameter mm
Solid box material volume — Solid box material volume using your entered measurements and assumptions.
Result = (((A × B) × C) ÷ 1000); A = Length mm, B = Width mm, C = Height mm
Solid cylinder material volume — Solid cylinder material volume using your entered measurements and assumptions.
Result = (((π × (A ^ 2)) × B) ÷ 1000); A = Radius mm, B = Height mm
Solid sphere material volume — Solid sphere material volume using your entered measurements and assumptions.
Result = ((((4 ÷ 3) × π) × (A ^ 3)) ÷ 1000); A = Radius mm
Open tube wall volume — Open tube wall volume using your entered measurements and assumptions.
Result = (((π × ((A ^ 2) - (B ^ 2))) × C) ÷ 1000); A = Outer radius mm, B = Inner radius mm, C = Length mm
Solid part mass estimate — Solid part mass estimate using your entered measurements and assumptions.
Result = (A × B); A = Solid volume cm³, B = Material density g/cm³
Infill core material estimate — Infill core material estimate using your entered measurements and assumptions.
Result = (A × (B ÷ 100)); A = Interior core volume cm³, B = Infill volume share %
Uniform scale volume multiplier — Uniform scale volume multiplier using your entered measurements and assumptions.
Result = (A ^ 3); A = Linear scale multiplier
Uniform scale area multiplier — Uniform scale area multiplier using your entered measurements and assumptions.
Result = (A ^ 2); A = Linear scale multiplier
Scaled part dimension — Scaled part dimension using your entered measurements and assumptions.
Result = (A × B); A = Original dimension mm, B = Linear scale multiplier
Rectangular build plate diagonal — Rectangular build plate diagonal using your entered measurements and assumptions.
Result = sqrt(((A ^ 2) + (B ^ 2))); A = Plate length mm, B = Plate width mm
Measured axis correction factor — Measured axis correction factor using your entered measurements and assumptions.
Result = (A ÷ B); A = Target travel mm, B = Measured travel mm
Mathematical axis steps correction — Mathematical axis steps correction using your entered measurements and assumptions.
Result = ((A × B) ÷ C); A = Current steps/mm, B = Commanded travel mm, C = Measured travel mm
Mathematical extrusion steps correction — Mathematical extrusion steps correction using your entered measurements and assumptions.
Result = ((A × B) ÷ C); A = Current steps/mm, B = Commanded feed mm, C = Measured feed mm
Printed dimension signed error — Printed dimension signed error using your entered measurements and assumptions.
Result = (A - B); A = Measured dimension mm, B = Target dimension mm
Printed dimension signed percent error — Printed dimension signed percent error using your entered measurements and assumptions.
Result = (((A - B) ÷ B) × 100); A = Measured dimension mm, B = Target dimension mm
Measured linear shrink share — Measured linear shrink share using your entered measurements and assumptions.
Result = (((A - B) ÷ A) × 100); A = Original dimension mm, B = Final dimension mm
Mathematical shrink compensation — Mathematical shrink compensation using your entered measurements and assumptions.
Result = (A ÷ B); A = Original dimension mm, B = Final measured dimension mm
Measured wall flow comparison — Measured wall flow comparison using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Target wall thickness mm, B = Measured wall thickness mm
Printed hole diameter error — Printed hole diameter error using your entered measurements and assumptions.
Result = (A - B); A = Measured hole mm, B = Target hole mm
Diametral fit clearance — Diametral fit clearance using your entered measurements and assumptions.
Result = (A - B); A = Hole diameter mm, B = Shaft diameter mm
Print electricity estimate — Print electricity estimate using your entered measurements and assumptions.
Result = ((A × B) ÷ 1000); A = Measured average watts, B = Print hours
Print electricity cost — Print electricity cost using your entered measurements and assumptions.
Result = (A × B); A = Energy kWh, B = Cost per kWh
Machine cost allocation per print — Machine cost allocation per print using your entered measurements and assumptions.
Result = ((A ÷ B) × C); A = Machine cost, B = Planned operating life hours, C = Print hours
Print handling labor cost — Print handling labor cost using your entered measurements and assumptions.
Result = ((A ÷ 60) × B); A = Hands-on minutes, B = Hourly cost
Print job cost subtotal — Print job cost subtotal using your entered measurements and assumptions.
Result = (((A + B) + C) + D); A = Material cost, B = Electricity cost, C = Machine allocation, D = Labor cost
Print quote with markup — Print quote with markup using your entered measurements and assumptions.
Result = (A × (1 + (B ÷ 100))); A = Job cost, B = Markup %
Sequential print batch time — Sequential print batch time using your entered measurements and assumptions.
Result = ((A × B) + C); A = Print hours per unit, B = Units, C = Setup hours
Measured print completion rate — Measured print completion rate using your entered measurements and assumptions.
Result = ((A ÷ B) × 100); A = Completed usable prints, B = Started prints
Failed print material cost — Failed print material cost using your entered measurements and assumptions.
Result = (A × B); A = Failed material g, B = Cost per gram
Expected starts from historical yield — Expected starts from historical yield using your entered measurements and assumptions.
Result = ceil((A ÷ (B ÷ 100))); A = Needed usable units, B = Historical success share %

Definitions and source references

Unit definitions and selected model references:

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