Taper Calculator
Calculate all critical taper dimensions for machining, engineering, and fabrication. Enter the large diameter, small diameter, and length of the taper. Get the taper per inch (TPI), taper per foot (TPF), taper ratio, half-angle, full included angle, midpoint diameter, diameter difference, and the closest Morse taper standard. Essential for lathe work, shaft design, pin tapers, and machine tool setup.
Diameter at the larger end
Diameter at the smaller end
Length along the axis from large to small end
Taper per Inch (TPI) = (D − d) ÷ L
Taper per Foot (TPF) = TPI × 12
Taper Ratio = 1 : L/(D−d)
Half-Angle = arctan((D−d) ÷ (2L))
Full Included Angle = 2 × Half-Angle
Midpoint Diameter = D − TPI × (L/2)
Where:
D = Large diameter
d = Small diameter
L = Length of taper
A shaft tapers from 2.000″ to 1.750″ over 6.000″.
TPI = (2.000 − 1.750) ÷ 6.000 = 0.04167″ per inch
TPF = 0.04167 × 12 = 0.5000″ per foot
Taper Ratio = 1:24
Half-Angle = arctan(0.250 ÷ 12) = arctan(0.02083) = 1.194°
Full Included Angle = 2.387°
Closest Morse Taper: N/A (different from MT standards)
Example — Construction Taper:
Concrete column: 24″ at base, 18″ at top, 120″ tall.
TPF = (24 − 18) ÷ 120 × 12 = 0.600″ per foot
Half-Angle = arctan((24−18)/(2×120)) = arctan(0.025) = 1.43°
How is taper calculated?
Taper is calculated as the reduction in diameter per unit length. Taper per foot (TPF) = (D - d) / L × 12, where D is the large diameter, d is the small diameter, and L is the length in inches. Taper per inch (TPI) = (D - d) / L. The taper angle (half-angle from centerline) = arctan((D - d) / (2L)). For example, a shaft going from 2" to 1.5" over 6 inches: TPF = (2 - 1.5) / 6 × 12 = 1.0 inch per foot.
What is a standard machine taper?
Common standard tapers include: Morse Taper (MT) — MT1: 0.5986" per ft, MT2: 0.5994" per ft, MT3: 0.6024" per ft, MT4: 0.6233" per ft, MT5: 0.6315" per ft. Brown & Sharpe Taper — B&S 9: 0.5029" per ft, B&S 10: 0.5161" per ft. Jarno Taper: 0.600" per ft in inch sizes (#2 = 0.200" at small end). Jacobs Taper for drill chucks. Standard Pin Taper: 1/4" per foot. These standards ensure interchangeability between machine tools and accessories.
What is the difference between taper and slope?
Taper is the change in diameter per unit length, typically used for round shafts, pins, and machine tapers. It considers the full diameter change. Slope is the change in radius per unit length, or the change in elevation for ramps and grades. For a round taper, slope = taper / 2. In machining, taper is often specified as inches per foot (e.g., 3/4" per foot). In construction, slope is specified as a ratio (e.g., 1:12). Both are related: a 1" per foot taper equals a slope of 0.5" per foot on each side.
How do I cut a taper on a lathe?
Several methods: 1) Compound rest method — set the compound rest to half the taper angle (arctan((D-d)/(2L))). 2) Tailstock offset method — offset the tailstock by (D-d)×L_total/(2L_taper) for long work between centers. 3) Taper attachment — follow the taper bar set to the desired angle. 4) CNC programming — use G-code taper cycles. For accurate tapers, use a taper micrometer or ring gauge. Calculate the offset carefully — too much offset affects center alignment and can cause chatter.
🔗 Related Calculators
📐 Formula
Taper per Inch (TPI) = (D − d) ÷ L
Taper per Foot (TPF) = TPI × 12
Taper Ratio = 1 : L/(D−d)
Half-Angle = arctan((D−d) ÷ (2L))
Full Included Angle = 2 × Half-Angle
Midpoint Diameter = D − TPI × (L/2)
Where:
D = Large diameter
d = Small diameter
L = Length of taper
📝 Example Calculation
A shaft tapers from 2.000″ to 1.750″ over 6.000″.
TPI = (2.000 − 1.750) ÷ 6.000 = 0.04167″ per inch
TPF = 0.04167 × 12 = 0.5000″ per foot
Taper Ratio = 1:24
Half-Angle = arctan(0.250 ÷ 12) = arctan(0.02083) = 1.194°
Full Included Angle = 2.387°
Closest Morse Taper: N/A (different from MT standards)
Example — Construction Taper:
Concrete column: 24″ at base, 18″ at top, 120″ tall.
TPF = (24 − 18) ÷ 120 × 12 = 0.600″ per foot
Half-Angle = arctan((24−18)/(2×120)) = arctan(0.025) = 1.43°