Taper Calculator – Calculate Precise Taper Ratios

Our handy taper calculator is used to determine the gradual narrowing or widening of cylindrical objects and helps in calculating the angle, diameter change, and length of tapered sections.

A digital taper calculator allow you to input the larger diameter, smaller diameter, and length of a tapered section. It then uses these values to compute the taper angle and rate of taper.

Taper Calculator

Initial Diameter (mm)	Final Diameter (mm)	Length (mm)	Taper (mm/mm)	Taper Angle (°)
50	45	100	0.05	1.43
80	60	200	0.10	2.86
100	90	250	0.04	1.15
30	25	50	0.10	2.86
60	40	100	0.20	5.71

Taper Calculation Formula

The fundamental taper calculation formula is:

Taper = (D - d) / L

Where:

• D = Larger diameter
• d = Smaller diameter
• L = Length of the tapered section

This formula yields the taper per unit length.

To obtain the taper angle, we use:

Taper Angle = arctan((D - d) / (2 * L))

A shaft with a larger diameter of 50mm, smaller diameter of 30mm, and length of 100mm.

• Taper = (50 – 30) / 100 = 0.2 mm/mm
• Taper Angle = arctan((50 – 30) / (2 * 100)) ≈ 5.71°

How do you calculate taper?

Calculating taper involves several steps:

• Measure the larger and smaller diameters
• Determine the length of the tapered section
• Apply the taper formula
• Convert to desired units if necessary

A conical flask has a base diameter of 15cm, top diameter of 5cm, and height of 25cm.

• D = 15cm, d = 5cm, L = 25cm
• Taper = (15 – 5) / 25 = 0.4 cm/cm
• Taper Angle = arctan((15 – 5) / (2 * 25)) ≈ 11.31°

What is the taper turning formula?

The taper turning formula is used in lathe operations to determine the compound slide angle for creating tapers:

Compound Slide Angle = arctan((D - d) / (2 * L))

This formula is identical to the taper angle calculation.

To turn a taper from 40mm to 35mm over a length of 50mm:

Compound Slide Angle = arctan((40 - 35) / (2 * 50)) ≈ 2.86°

How many degrees is a taper per foot?

Taper is often expressed in degrees per foot for standardization. To convert taper per unit length to degrees per foot:

Degrees per foot = arctan(Taper) * (180 / π) * 12

A taper of 1/4 inch per foot:

• Taper = 1/4 inch / 12 inches = 0.0208
• Degrees per foot = arctan(0.0208) (180 / π) 12 ≈ 1.19°

How to calculate taper 1:50?

A taper ratio of 1:50 means the diameter changes by 1 unit for every 50 units of length.

To calculate Convert the ratio to decimal: 1/50 = 0.02

For a 1:50 taper over 200mm:

Taper = 0.02

Diameter change = 0.02 * 200 = 4mm

If starting diameter is 30mm, end diameter is 26mm

Taper Angle = arctan(0.02 / 2) ≈ 0.57°

Sources / References

• Machinery’s Handbook Guide

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