Sine Bar Precision Measurement A Beginner’s Guide to 7 Types [PDF]

Hello everyone, In this article I shall talk about the history, uses, types, of Sine Bars, and how it’s made. I’ll also cover how it works and its pros, cons, and uses. A downloadable PDF is also given at the very end.

I am a mechanical engineer. Precision matters a lot. Exact measurements are important. We use a tool called a sine bar. It helps measure angles accurately.

What is a Sine Bar

The sine bar is a highly accurate tool used in engineering and manufacturing. It’s like a long metal bar with two blocks fixed on it, forming a “T” shape. These blocks are carefully placed to be perfectly straight.

The Construction is Sturdy and Robust and fights corrosion easily, this tool can last a long time while maintaining its accuracy. It’s commonly used when there’s a need to measure angles very precisely, such as in machining, grinding, or quality checks.

To use it, you apply a bit of math involving triangles. It’s paired with a special gauge or measuring tool to determine angles with extreme precision. This is a significant aid in ensuring precise measurements and alignments in engineering and manufacturing processes.

Sine Bar
What is Sine Bar
Sine Bar Diagram
Sine Bar Parts
Sine Bar Components

History of Sine Bar

Talking about the history of the sine bar, Long ago, in the early 1800s, a brilliant Swiss mathematician named Johann Bernoulli developed a way for properly calculating angles. He utilized a bar with two precisely positioned cylinders on it.

This concept was improved as time went on, becoming a device that could precisely measure angles. The advancement was necessary given the need to know angles very precisely to make precise machine parts for the best machining results.

Today, the sine bar serves different sectors. Used to calibrate equipment so that machines function seamlessly and parts are always within defined sizes and shapes.

Purpose of Sine Bar

The Purposes of Sine Bar are as follows

Accurate Angle Measurement: Imagine needing to measure angles with laser-like precision. That’s where the sine bar shines. It’s the go-to tool when we can’t compromise on accuracy, whether we’re crafting machine parts or inspecting high-precision components.

Versatility: Think of the sine bar as your multi-tool. It’s not limited to one job; it’s the MVP in engineering, machining, and metrology. Its versatility means it can tackle a wide range of tasks in different industries.

Measuring Small and Big Things: Big or small, the sine bar handles them all! It’s the ultimate size-agnostic tool. Whether you’re dealing with a tiny widget or a massive machine, the sine bar delivers pinpoint angle measurements every time.

Consistency: Trust is key, and the sine bar has it in spades. It’s your unwavering ally for consistent, spot-on measurements. You can count on it, no matter how many times you use it.

Efficiency: Time is money, and the sine bar knows it. When paired with high-tech measuring gear like a dial indicator or micrometer, it turbocharges your measurement process. Get ready to speed up production and inspection with ease.

Types of Sine Bar
Single Cylinder Sine Bar
Double Cylinder Sine Bar
Plain Sine Bar
Compound Sine Bar
Universal Sine Bar
Angular Sine Bar
Magnetic Sine Bar

Types of Sine Bar

There are different Types of Sine Bars are as follows

Single Cylinder Sine Bar: This one has just one cylinder attached to the bar.

Double Cylinder Sine Bar: Here, you’ve got two cylinders mounted on the bar.

Plain Sine Bar: This is a precision-ground bar with two equal cylinders set at a fixed distance. It’s used with a dial gauge or micrometer to measure angles accurately.

Compound Sine Bar: Think of this as two plain sine bars stacked on top of each other. It helps measure angles that can’t be evenly divided by the divisions on a plain bar.

Universal Sine Bar: This one’s versatile. It comes with two sets of cylinders that you can adjust. It’s handy for measuring angles of different sizes and shapes because you can change the distances between the cylinders.

Angular Sine Bar: This has two arms that can move to different angles. It’s used when you need to measure angles that the plain sine bar can’t handle.

Magnetic Sine Bar: Similar to the plain sine bar, but it has a magnetic base. This makes it easy to attach to things quickly, which is useful when inspecting machined parts.

Parts and Construction of Sine Bar

The Parts of Sine Bar are as follows

  • Bar: Precision-ground main body for angle measurement.
  • Cylinders: Two hardened steel or tungsten carbide cylinders mounted parallel and perpendicular to the bar, forming reference planes.
  • Base: Flat support surface (steel, granite, etc.) for stability during measurements, with magnetic, clamping, or bolting options.
  • Gauge pins: Hardened steel pins set the cylinder distance accurately.
  • Vernier scale: Graduated scale for high-precision angle measurement, with a sliding Vernier scale for finer readings.
  • Dial gauge or micrometer: Attached to the bar or base for accurate angle deviation measurement.

Working Principle of Sine Bar

The fundamental principle behind a sine bar relies on the core principles of trigonometry. When one end of the sine bar rests on a surface plate and the other is set at the height of the slip gauge, it forms a triangular arrangement involving the sine bar, surface plate, and slip gauge.

The longest side of this triangle corresponds to the sine bar itself, formed by connecting the vertical slip gauges with the surface plate’s base. If we designate the slip gauge height as ‘H’ and the length of the sine bar as ‘L,’ the sine ratio can be expressed as H divided by the length ‘L’ times the sine of angle θ.

Consequently, we can determine the angle θ by calculating the inverse sine (sin⁻¹) of H divided by L, enabling precise measurement of angles.

Sine Bar Working 
Sine Bar Working Principle
Working Principle of Sine Bar

Working when the angle of a small component is to be measured

For small components, place the object on the cylinders, position the sine bar on top, use a dial gauge or micrometer to measure the object’s height, measure the cylinder distance, and calculate the angle using the formula

Angle = sin-1 (Height/Diameter).

Working when the angle of a large component is to be measured

For large components, place the object on support, position the sine bar on top, place the cylinders on the object, use a dial gauge or micrometer to measure the object’s height, measure the cylinder distance, and calculate the angle using the formula

Angle = tan-1 (Height/Distance).

How to Use a Sine Bar

Video By PracticlMachinist

Comparison: Sine Bar vs. Protractor

ParameterSine BarProtractor
PurposeUsed for precise angle measurement and setupMeasures angles in diverse applications
StructureComprises a sturdy steel gauge body with two rollersTypically flat, semi-circular, or circular with degree markings
PrecisionOffers high precision for angular measurementsGenerally provides lower precision compared to sine bars
Use with ComponentsUsed with slip gauges and elevation gauges for accuracyTypically employed independently for angle measurement
Measuring RangeLimited to specific angles determined by its lengthGenerally offers a full 360-degree measuring range
ApplicationCommonly used in machining for precise angle setupsWidely applied in various fields for angle measurement and setting
Specialized ApplicationsUtilized for specialized tasks requiring precise angular measurementsApplied in a wide range of general angle measurement scenarios
Common UsageProminent in machining and engineering applicationsCommonly utilized in construction, carpentry, and general measurement tasks

Advantages of Sine Bar

  • Highly accurate tool for precise angle measurements.
  • Suitable for measuring angles on both small and large objects.
  • Durable and can last for many years with proper care.

Disadvantages of Sine Bar

  • Limited to specific angles based on its length.
  • Requires additional tools like slip gauges for precision.
  • Not suitable for very small or large angles.
  • Susceptible to wear and damage affecting accuracy.
  • More complex setup compared to basic protractors.

Applications of Sine Bar

  • Ideal for precise angle measurement in machining.
  • Useful for aligning objects at specific angles.
  • Aids in verifying flatness and parallelism of surfaces.
  • Ensures accurate setups in manufacturing and engineering.
  • Used for calibration of other measuring tools.


How is Sine bar Manufactured

The sine bar is crafted from high-quality steel, which is heat-treated, ground, and polished with precision. It undergoes calibration and receives engraved angle markings. Skilled craftsmanship is vital to ensure its accuracy and reliability.

How to set a sine bar

Clean the surfaces, adjust the height, clamp securely, check the level, measure the angle, and maintain stability for accuracy.

What are the possible errors one can counter using sine bars

  • Parallax error (misaligned eye).
  • Angular tilt error (not horizontal).
  • Height measurement error (wrong gauge blocks).
  • Workpiece placement error (incorrect placement).
  • Sine bar accuracy error (manufacturing).

What is Sine Center

A sine center is employed to determine the centers of cylindrical or conical workpieces.

What is the range of the sine bar?

The sine bar’s range commonly encompasses standard lengths such as 100 mm, 200 mm, or 300 mm, offering precise angular measurements within these distances.

What is Sine Bar Formula

The sine bar formula is expressed as θ = sin^(-1)(H/L), where θ represents the angle, H is the height of the slip gauges, and L is the length of the sine bar.


I hope my guide helped you understand what are sine bars, their purpose, history, pros, cons, and application. If you have any doubts feel free to write to us in the comment box below. Check out our other articles too.


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