Plane Angle Converter
Our plane angle converter helps you convert between 10 angle units including degrees, radians, gradians, minutes and seconds of arc, milliradians, and more. Fast, accurate, and works instantly in your browser. Perfect for mathematics, engineering, navigation, and astronomy.
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10 Angle Units
Convert between degrees, radians, gradians, minutes and seconds of arc, milliradians, turns, quadrants, sextants, and octants.
Instant Conversion
All conversions happen instantly in your browser using precise mathematical calculations. No server delays, no API calls—just instant results.
100% Private
All conversions happen locally in your browser. We never store, log, or transmit your conversion data. Complete privacy guaranteed.
Plane Angle Converter online
Convert between 10 angle units with instant, precise calculations
Understanding Plane Angle Units
Plane angle units measure the rotation between two lines meeting at a point. Understanding each unit's origin, common applications, and relationships helps you choose the right unit for your needs and make accurate conversions. Here's a comprehensive guide to all angle units supported by our converter.
📐Common Angle Units
Picosecond (ps)
Definition: One picosecond equals 1 trillionth of a second (1/1,000,000,000,000 second or 10⁻¹² seconds). The prefix "pico" means one trillionth in the metric system.
Common Uses: Picoseconds are used in ultrafast physics, laser science, and advanced electronics. Examples include: ultrafast laser pulses, molecular dynamics simulations, quantum computing operations, high-speed electronics timing, and atomic-scale processes. Light travels approximately 0.3 millimeters (0.012 inches) in one picosecond in a vacuum. This unit is essential for studying processes that occur at the atomic and molecular level.
Conversion: 1 ps = 0.000000000001 s = 0.001 ns = 1,000 fs
Nanosecond (ns)
Definition: One nanosecond equals 1 billionth of a second (1/1,000,000,000 second or 10⁻⁹ seconds). The prefix "nano" means one billionth in the metric system.
Common Uses: Nanoseconds are used in computer science, electronics, and physics. Examples include: computer processor clock cycles (modern CPUs operate at gigahertz frequencies, where each cycle is measured in nanoseconds), memory access times, network latency measurements, laser pulse durations, and quantum physics experiments. Light travels approximately 30 centimeters (11.8 inches) in one nanosecond in a vacuum.
Conversion: 1 ns = 0.000000001 s = 0.000001 ms = 0.001 μs
Microsecond (μs)
Definition: One microsecond equals 1 millionth of a second (1/1,000,000 second or 10⁻⁶ seconds). The prefix "micro" means one millionth in the metric system.
Common Uses: Microseconds are used in electronics, telecommunications, and scientific measurements. Examples include: radio frequency timing, audio signal processing, camera shutter speeds (some high-speed cameras capture images in microseconds), radar systems, and timing measurements in physics experiments. Light travels approximately 300 meters (984 feet) in one microsecond in a vacuum.
Conversion: 1 μs = 0.000001 s = 0.001 ms = 1,000 ns
Millisecond (ms)
Definition: One millisecond equals 1 thousandth of a second (1/1,000 second or 10⁻³ seconds). The prefix "milli" means one thousandth in the metric system.
Common Uses: Milliseconds are commonly used in computing, sports timing, and everyday measurements. Examples include: computer response times, video game frame rates (60 FPS = 16.67 ms per frame), reaction time measurements, stopwatch precision, audio latency, and network ping times. Human reaction time is typically 150-300 milliseconds. A typical blink of an eye takes 100-400 milliseconds.
Conversion: 1 ms = 0.001 s = 1,000 μs = 1,000,000 ns
⏰Standard Time Units (SI Base)
Second (s)
Definition: The second is the base unit of time in the International System of Units (SI). It is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
History: The modern definition of the second was adopted in 1967, replacing the older definition based on the Earth's rotation. This atomic definition provides extreme precision and stability, making it the foundation for all time measurements worldwide. The second is one of the seven base units in the SI system.
Common Uses: Seconds are the most fundamental time unit, used in all scientific, engineering, and everyday applications. Examples include: scientific measurements, sports timing, cooking timers, countdown timers, and all time-based calculations. The heartbeat of an average adult at rest is approximately 60-100 beats per minute, or about 0.6-1 second per beat.
Conversion: 1 s = 1,000 ms = 1,000,000 μs = 1,000,000,000 ns
Minute (min)
Definition: One minute equals 60 seconds. The minute is not an official SI unit but is accepted for use with SI units. It's one of the most commonly used time units in everyday life.
History: The minute has been used since ancient times, originally derived from dividing an hour into 60 parts (following the Babylonian sexagesimal system). The word "minute" comes from the Latin "pars minuta prima" meaning "first small part."
Common Uses: Minutes are used extensively in everyday life for timing activities, meetings, cooking, exercise, and scheduling. Examples include: meeting durations (30-minute meetings), cooking times (bake for 45 minutes), exercise intervals (run for 20 minutes), and time estimates. Most people think in minutes for short to medium-duration activities.
Conversion: 1 min = 60 s = 0.0167 hours
Hour (h)
Definition: One hour equals 60 minutes or 3,600 seconds. Like the minute, the hour is not an official SI unit but is accepted for use with SI units and is fundamental to our daily timekeeping.
History: The hour has been used since ancient civilizations, with the 24-hour day being divided into 12 hours of daylight and 12 hours of darkness (though the length varied with seasons). The modern equal-length hour became standard with mechanical clocks in the Middle Ages.
Common Uses: Hours are the standard unit for work schedules, travel time, and longer activities. Examples include: work shifts (8-hour workday), travel time (2-hour flight), movie durations (90-minute to 3-hour films), sleep duration (7-9 hours per night), and hourly wages. The average human sleeps 7-9 hours per day.
Conversion: 1 h = 60 min = 3,600 s = 0.0417 days
📅Calendar Time Units
Day (d)
Definition: One day equals 24 hours or 86,400 seconds. A day represents one complete rotation of the Earth on its axis relative to the Sun (solar day).
History: The concept of a day is one of the oldest time measurements, based on the natural cycle of day and night. The 24-hour division comes from ancient Egyptian and Babylonian systems. The modern definition is based on the mean solar day.
Common Uses: Days are fundamental to human life and scheduling. Examples include: project timelines (5-day workweek), medication schedules (take twice daily), vacation planning (7-day trip), and age calculations. Most people organize their lives around daily cycles of work, rest, and activities.
Conversion: 1 d = 24 h = 1,440 min = 86,400 s
Week (wk)
Definition: One week equals 7 days or 604,800 seconds. The week is a cultural and religious time unit, not based on astronomical cycles.
History: The 7-day week has ancient origins, possibly from the Babylonians who associated each day with a celestial body. It was adopted by many cultures and is now the standard work and rest cycle in most of the world.
Common Uses: Weeks are used for scheduling, planning, and recurring cycles. Examples include: work schedules (40-hour workweek), pregnancy tracking (measured in weeks), project timelines (2-week sprint), pay periods (bi-weekly), and course schedules (10-week semester). Most calendars and planners are organized by weeks.
Conversion: 1 wk = 7 d = 168 h = 604,800 s
Fortnight
Definition: One fortnight equals 14 days or 1,209,600 seconds. The word "fortnight" comes from "fourteen nights" and is commonly used in British English and some Commonwealth countries.
History: The fortnight has been used since Middle English times and remains a standard unit in many English-speaking countries outside North America. It's particularly common in the UK, Australia, and New Zealand for scheduling and planning purposes.
Common Uses: Fortnights are used for bi-weekly scheduling, pay periods, and project planning. Examples include: bi-weekly pay periods (paid every fortnight), rental agreements (fortnightly rent), project milestones, and vacation planning. Many businesses and organizations use fortnightly cycles for operations and reporting.
Conversion: 1 fortnight = 14 d = 336 h = 1,209,600 s = 2 weeks
Month (30 days)
Definition: One month equals 30 days or 2,592,000 seconds. This is a standardized month used for calculations, as actual calendar months vary in length (28-31 days).
Note: Calendar months have different lengths: 28-31 days depending on the month and whether it's a leap year. For conversion purposes, we use 30 days as a standard average, which is commonly used in business and financial calculations.
Common Uses: Months are used for billing cycles, subscriptions, and medium-term planning. Examples include: monthly subscriptions, rent payments, billing cycles, project milestones, and age calculations (especially for babies and young children). Most financial and business operations use monthly cycles.
Conversion: 1 mo (30 days) = 30 d = 720 h = 2,592,000 s
Quarter (3 months)
Definition: One quarter equals 3 months or 90 days (7,776,000 seconds). This is a standard business and financial time unit.
Common Uses: Quarters are fundamental to business, finance, and corporate reporting. Examples include: quarterly earnings reports (Q1, Q2, Q3, Q4), fiscal year planning, quarterly goals and reviews, stock market analysis, and business performance metrics. Most publicly traded companies report financial results quarterly. Academic years are often divided into quarters in some educational systems.
Business Context: The business year is typically divided into four quarters: Q1 (January-March), Q2 (April-June), Q3 (July-September), and Q4 (October-December). Quarterly reporting is required for public companies and provides regular updates on financial performance.
Conversion: 1 quarter = 3 mo = 90 d = 2,160 h = 7,776,000 s
Year (365 days)
Definition: One year equals 365 days or 31,536,000 seconds. This represents a common year (non-leap year) in the Gregorian calendar.
Note: A leap year has 366 days (31,622,400 seconds) to account for the approximately 365.25 days it takes Earth to orbit the Sun. For conversion purposes, we use 365 days as the standard, which is accurate for most calculations.
Common Uses: Years are fundamental to age, history, and long-term planning. Examples include: age calculations, historical dates, annual reports, yearly goals, and long-term investments. The average human lifespan is approximately 70-80 years. Most major life events and milestones are measured in years.
Conversion: 1 yr (365 days) = 365 d = 8,760 h = 31,536,000 s = 4 quarters
🌍Long-Term Time Units
Decade
Definition: One decade equals 10 years or 315,360,000 seconds (based on 365-day years).
Common Uses: Decades are used for historical periods, generational analysis, and long-term trends. Examples include: historical eras (the 1960s, the 1990s), generational cohorts (millennials, Gen Z), economic cycles, and long-term planning. Decades help organize history and cultural trends into manageable periods.
Conversion: 1 decade = 10 yr = 3,650 d = 315,360,000 s
Century
Definition: One century equals 100 years or 3,153,600,000 seconds (based on 365-day years).
Common Uses: Centuries are used for major historical periods, geological time scales, and very long-term planning. Examples include: historical eras (20th century, 21st century), architectural lifespans, long-term environmental changes, and generational family histories. Most major historical events and cultural shifts are measured in centuries.
Historical Context: The 20th century (1901-2000) saw two world wars, space exploration, and the digital revolution. The 21st century (2001-2100) is marked by globalization, climate change awareness, and rapid technological advancement.
Conversion: 1 century = 100 yr = 36,500 d = 3,153,600,000 s = 10 decades
Millennium
Definition: One millennium equals 1,000 years or 31,536,000,000 seconds (based on 365-day years). The word "millennium" comes from Latin "mille" (thousand) and "annus" (year).
Common Uses: Millenniums are used for very long-term historical periods, geological time scales, and major cultural epochs. Examples include: major historical transitions (the turn of the millennium in 2000), geological eras, long-term climate studies, and civilization timelines. The concept of millennia helps organize human history into major epochs and cultural periods.
Historical Context: The first millennium CE (1-1000) saw the rise and fall of empires, the spread of major religions, and significant cultural developments. The second millennium (1001-2000) included the Renaissance, Industrial Revolution, and modern era. The third millennium (2001-3000) is just beginning and will see continued technological and social evolution.
Conversion: 1 millennium = 1,000 yr = 365,000 d = 10 centuries = 100 decades
Quick Reference: Time Unit Equivalents
| Unit | Seconds | Minutes | Hours |
|---|---|---|---|
| 1 Nanosecond | 0.000000001 s | 1.67×10⁻¹¹ min | 2.78×10⁻¹³ h |
| 1 Microsecond | 0.000001 s | 1.67×10⁻⁸ min | 2.78×10⁻¹⁰ h |
| 1 Millisecond | 0.001 s | 0.0000167 min | 0.000000278 h |
| 1 Second | 1 s | 0.0167 min | 0.000278 h |
| 1 Minute | 60 s | 1 min | 0.0167 h |
| 1 Hour | 3,600 s | 60 min | 1 h |
| 1 Day | 86,400 s | 1,440 min | 24 h |
| 1 Week | 604,800 s | 10,080 min | 168 h |
| 1 Year (365 days) | 31,536,000 s | 525,600 min | 8,760 h |
| 1 Decade | 315,360,000 s | 5,256,000 min | 87,600 h |
| 1 Century | 3,153,600,000 s | 52,560,000 min | 876,000 h |
| 1 Millennium | 31,536,000,000 s | 525,600,000 min | 8,760,000 h |
What is Plane Angle Conversion?
Plane angle conversion is the process of converting an angle measurement from one unit to another. Plane angles measure the rotation between two lines meeting at a point (vertex). Understanding how to convert between different angle units is essential for mathematics, engineering, navigation, astronomy, and scientific research.
Angle units range from the very precise (seconds of arc, used in astronomy) to the large (turns or revolutions). The most commonly used angle units include degrees, radians, and gradians. Degrees are most common in everyday use, radians are the SI base unit and standard in mathematics and physics, and gradians are used in some metric system applications. Each unit has a precise mathematical relationship to the others, with the radian being the base unit in the International System of Units (SI).
According to the International Bureau of Weights and Measures (BIPM), the radian is the SI base unit for plane angle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle equals 2π radians (approximately 6.28318 radians) or 360 degrees. This precise definition allows for accurate conversions between all angle units using mathematical relationships based on π.
✗Manual Calculation
- • Complex π calculations
- • Risk of calculation errors
- • Difficult to remember formulas
- • Time-consuming for conversions
✓Online Angle Converter
- • Instant conversion results
- • Precise Math.PI calculations
- • All angle units supported
- • Supports 10 angle units
Angle Conversion Facts
Interesting facts about angle units and their relationships
Angle Measurement Standards
According to the International Bureau of Weights and Measures (BIPM), the radian is the base unit for plane angle in the International System of Units (SI). One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. All angle conversions are based on precise mathematical relationships using π, ensuring accuracy across all angle unit conversions from seconds of arc to full revolutions.
Why Use Our Plane Angle Converter?
Our plane angle converter provides instant, accurate conversions between 10 angle units with high precision. Whether you're working on mathematical problems, engineering projects, navigation, or astronomy, our tool offers the speed, accuracy, and convenience you need.
Instant Client-Side Conversion
All time conversions happen instantly in your browser using precise mathematical calculations. No server delays, no API calls, no waiting—just instant results whenever you need them. Perfect for quick calculations, programming tasks, and scientific work where speed matters.
10 Comprehensive Angle Units
Convert between degrees, radians, gradians, minutes and seconds of arc, milliradians, turns, quadrants, sextants, and octants. This comprehensive range covers everything from common mathematical measurements to specialized angular units used in navigation, astronomy, and engineering.
High-Precision Calculations
Our converter uses precise mathematical formulas based on the International System of Units (SI) definitions, using Math.PI for exact calculations. Conversions maintain high precision, making it suitable for mathematical calculations, trigonometric functions, engineering projects, navigation, and astronomy where accuracy is critical.
100% Private & Secure
All conversions happen locally in your browser. We never store, log, or transmit your conversion data. Your calculations remain completely private, making this tool safe for sensitive scientific or business calculations. No registration, no tracking, no data collection.
Completely Free Forever
Use our angle converter as much as you want, whenever you need it, without any cost. No hidden fees, no premium tiers, no usage limits. Convert angle units unlimited times for free, making it perfect for students, mathematicians, engineers, navigators, astronomers, and anyone who needs regular angle conversions.
Mobile-Friendly Design
Access our angle converter from any device—desktop, tablet, or smartphone. The responsive design works perfectly on all screen sizes, so you can convert angle units on the go. Perfect for students studying mathematics, engineers on job sites, navigators, or anyone who needs quick angle conversions anywhere.
How It Works
Our angle converter uses precise mathematical conversions based on the International System of Units (SI) definitions. All conversions are calculated client-side in your browser for instant results. Conversions use radians as the base unit with Math.PI for precision, ensuring accuracy across all angle measurements.
Select Units
Choose your source angle unit from the "Convert From" dropdown and your target angle unit from the "Convert To" dropdown.
Enter Amount
Type the amount you want to convert in the input field. You can enter whole numbers or decimals.
Calculate
Our converter calculates the conversion using precise mathematical formulas with Math.PI, converting to radians first, then to your target unit.
View Result
Click Convert to instantly see the converted amount displayed clearly with appropriate precision formatting.
Best Practices for Angle Conversion
When converting angle units, following best practices ensures you get accurate results and understand the relationships between different angle measurements. Here are essential tips for using angle converters effectively:
1. Understand Degree and Radian Relationships
The most important conversion to remember is that 180° = π radians. This means 1° = π/180 radians ≈ 0.017453 radians, and 1 radian = 180/π degrees ≈ 57.2958°. Degrees are most common in everyday use and navigation, while radians are standard in mathematics, physics, and most programming languages' trigonometric functions.
2. Use Radians for Trigonometric Functions
Most programming languages and mathematical functions use radians, not degrees. When working with trigonometric functions (sin, cos, tan) in code or calculators, always convert degrees to radians first. Our converter makes this easy - simply select degrees as source and radians as target.
3. Choose Appropriate Precision
Choose time units that make sense for your application. For computer science and programming, nanoseconds and milliseconds are common. For everyday use, seconds, minutes, and hours are most practical. For historical or geological contexts, years, decades, and centuries are appropriate.
4. Verify Large Number Conversions
When converting very large numbers (e.g., converting millions of seconds to years), verify the result makes sense. For example, 31,536,000 seconds equals 1 year, so 100,000,000 seconds equals approximately 3.17 years. Double-checking helps catch input errors.
5. Note Month and Year Definitions
Our converter uses standard definitions: 1 month = 30 days (2,592,000 seconds) and 1 year = 365 days (31,536,000 seconds). For precise calendar calculations, you may need to account for actual month lengths and leap years, but for most conversions, these standard values provide sufficient accuracy.
Frequently Asked Questions
How do I convert angle units online?
To convert angle units online, select your source angle unit from the 'Convert From' dropdown (e.g., degrees, radians, gradians), choose your target angle unit from the 'Convert To' dropdown, enter the angle value you want to convert, and click the Convert button. The tool will instantly display the converted angle using precise mathematical conversions.
What angle units are supported by this converter?
Our plane angle converter supports 10 angle units including degrees, radians, gradians, minutes of arc, seconds of arc, milliradians, turns (revolutions), quadrants, sextants, and octants. This comprehensive range covers everything from common mathematical measurements to specialized angular units used in navigation, astronomy, and engineering.
How accurate are the angle conversions?
Our angle converter uses precise mathematical conversions based on standard angle unit definitions. Conversions are calculated client-side in your browser using high-precision mathematics (Math.PI), ensuring accurate results. For example, 1 radian = 180/π degrees ≈ 57.2958°, 1 degree = π/180 radians, and 1 gradian = 0.9 degrees. The tool maintains accuracy across all unit conversions.
What is the difference between degrees, radians, and gradians?
Degrees, radians, and gradians are different units for measuring angles. A degree (°) divides a full circle into 360 parts (1° = 1/360 of a circle). A radian (rad) is the SI base unit and represents the angle subtended by an arc equal to the radius (1 full circle = 2π radians). A gradian (grad) divides a full circle into 400 parts (1 grad = 0.9°). Degrees are most common in everyday use, radians are standard in mathematics and physics, and gradians are used in some metric system applications.
Is this angle converter free to use?
Yes, our plane angle converter is completely free to use. There are no registration requirements, no hidden fees, and no limits on the number of conversions you can perform. Simply visit the page, enter your values, and convert angle units instantly without any cost.
How do I convert degrees to radians or radians to degrees?
To convert degrees to radians, select 'Degree' as the source unit and 'Radian' as the target unit, enter the number of degrees, and click Convert. The formula is: radians = degrees × (π/180). Similarly, to convert radians to degrees, select 'Radian' as the source and 'Degree' as the target. The formula is: degrees = radians × (180/π). The converter handles all angle unit conversions automatically with precise calculations.
Can I use this for trigonometric calculations and programming?
Absolutely! Our angle converter is perfect for mathematical calculations, trigonometry, and programming applications. It supports conversions between degrees and radians, which are essential for trigonometric functions in mathematics and programming. Most programming languages use radians for trigonometric functions, so converting degrees to radians (or vice versa) is a common need.
What are minutes and seconds of arc used for?
Minutes of arc (arcmin) and seconds of arc (arcsec) are smaller subdivisions of degrees used for precise angular measurements. One degree = 60 arcminutes, and one arcminute = 60 arcseconds. These units are commonly used in astronomy (to measure angular sizes and positions of celestial objects), navigation (for coordinates), surveying, and cartography. For example, the apparent size of the Moon is about 30 arcminutes, and precise star positions are measured in arcseconds.
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