Coriolis Effect Calculator
Last Updated: October 29, 2025
Calculate Coriolis force and acceleration from velocity and latitude using Earth's rotation parameters. Essential tool for meteorology, oceanography, physics education, and rotational dynamics analysis.
Calculator
Enter your motion parameters below to calculate Coriolis effects instantly.
Enter the velocity, latitude, and mass to determine the Coriolis force and acceleration.
Speed of the moving object relative to Earth's surface
Geographic latitude (-90° to 90°, positive for Northern Hemisphere)
Mass of the moving object (optional for acceleration only)
Results
Enter values to see results
Table of Contents
What is Coriolis Effect Calculator?
Understanding Earth's Rotation and Apparent Forces
The Coriolis Effect Calculator is a specialized physics tool that calculates the Coriolis force and acceleration experienced by objects moving on Earth's surface. The Coriolis effect is an apparent deflection of moving objects caused by Earth's rotation, resulting in curved paths relative to the rotating reference frame.
This calculator is essential for understanding atmospheric and oceanic circulation patterns, meteorology, ballistics, and physics education. It provides accurate calculations for Coriolis effects using velocity, latitude, and Earth's angular velocity parameters.
Key Concepts
Coriolis Force (F_c): Apparent force acting on moving objects in rotating reference frames, measured in Newtons (N). A fictitious force that appears when analyzing motion from Earth's rotating frame. Perpendicular to the velocity vector and causes deflection to the right in the Northern Hemisphere and left in the Southern Hemisphere.
Coriolis Acceleration (a_c): Acceleration due to Coriolis effect, measured in meters per second squared (m/s²). Related to force by F_c = ma_c. Describes the apparent acceleration experienced by objects moving relative to a rotating frame.
Velocity (v): Speed of object relative to Earth's rotating surface, measured in meters per second (m/s). The Coriolis effect is proportional to velocity - faster-moving objects experience greater deflection. Only the component of velocity perpendicular to Earth's rotation axis contributes.
Latitude (φ): Geographic latitude from equator, measured in degrees (-90° to 90°). The sine of latitude (sin φ) appears in the formula, making the effect zero at the equator (sin 0° = 0) and maximum at the poles (sin ±90° = ±1). This explains why weather patterns are most affected at mid-latitudes.
Earth's Angular Velocity (Ω): Constant value 7.292 × 10⁻⁵ rad/s, representing Earth's rotation rate. This is approximately 2π radians per 24 hours. The small value means Coriolis effects are subtle for short distances but accumulate over long ranges or times.
Physical Interpretation
The Coriolis effect is not a real force but an apparent force that appears when describing motion from a rotating reference frame (Earth). From an inertial frame, objects move in straight lines, but from Earth's rotating perspective, they appear to curve. The effect results from Earth's rotation and explains why objects moving north or south appear to deflect east or west. This deflection is to the right in the Northern Hemisphere and to the left in the Southern Hemisphere.
The formula F_c = 2mvΩ sin(φ) shows that Coriolis force increases with mass, velocity, and latitude. The factor 2 comes from the cross product in the full vector formulation. The sine of latitude means the effect is strongest at high latitudes (near the poles) and zero at the equator. This explains why hurricanes rotate counterclockwise in the Northern Hemisphere (deflecting right) and clockwise in the Southern Hemisphere (deflecting left).
Direction and Hemisphere Differences
In the Northern Hemisphere, moving objects deflect to the right. This means winds moving north curve east, and winds moving south curve west. In the Southern Hemisphere, deflection is to the left. This creates different rotation directions for weather systems: cyclones rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere. The effect is most noticeable for large-scale, long-duration motion like weather systems and ocean currents.
Historical Development
The Coriolis effect was first described by French mathematician Gaspard-Gustave de Coriolis in 1835 in his work on rotating reference frames. It explains why moving objects on Earth appear to curve, affecting weather patterns, ocean currents, and long-range projectile trajectories. The effect is zero at the equator and maximum at the poles. The understanding of Coriolis effect was crucial for developing accurate weather models, ocean circulation theory, and long-range ballistic calculations. It's also fundamental to inertial navigation systems and GPS corrections.
Units and Magnitude
Force Unit: N (Newton) - same as any force
Acceleration Unit: m/s² - same as any acceleration
Earth's Angular Velocity: Ω = 7.292 × 10⁻⁵ rad/s (constant)
Typical Magnitudes: Coriolis acceleration is typically small (10⁻⁴ to 10⁻² m/s²) but accumulates over long distances or times
Latitude Factor: sin(φ) ranges from 0 (equator) to ±1 (poles), making effect strongest at high latitudes
Formulas and Equations
Coriolis Effect Calculation Methods
1. Coriolis Force
F_c = 2mvΩ sin(φ)
Where:
- • F_c = Coriolis force (N)
- • m = Mass (kg)
- • v = Velocity (m/s)
- • Ω = Earth's angular velocity = 7.292 × 10⁻⁵ rad/s
- • φ = Latitude (degrees)
Use case: Calculate the Coriolis force on a moving object. This apparent force causes deflection perpendicular to the velocity direction. The force is proportional to mass, velocity, and the sine of latitude. Essential for analyzing long-range projectiles, understanding weather patterns, and predicting ocean current behavior. The force is zero at the equator and maximum at the poles.
2. Coriolis Acceleration
a_c = 2vΩ sin(φ)
Where:
- • a_c = Coriolis acceleration (m/s²)
- • v = Velocity (m/s)
- • Ω = Earth's angular velocity = 7.292 × 10⁻⁵ rad/s
- • φ = Latitude (degrees)
Use case: Calculate Coriolis acceleration without needing mass. Related to force by F_c = ma_c. This acceleration describes how much an object's path curves due to Earth's rotation. Useful for trajectory calculations, navigation corrections, and understanding the magnitude of deflection. The acceleration is independent of mass, making it useful for both light and heavy objects.
Applications of Coriolis Effect
Real-World Uses Across Industries
Coriolis effect calculations are essential across numerous physics, meteorology, and geophysics fields. Here's a comprehensive overview of practical applications:
| Industry | Applications | Importance |
|---|---|---|
| Meteorology | Weather patterns, cyclone rotation, atmospheric circulation, wind deflection, storm formation, jet streams, trade winds | Critical for weather prediction, climate modeling, and understanding atmospheric dynamics |
| Oceanography | Ocean currents, gyres, water circulation patterns, upwelling, downwelling, Ekman transport, ocean basin circulation | Essential for climate modeling, marine ecosystem understanding, and ocean current prediction |
| Ballistics | Long-range projectiles, artillery trajectories, missile guidance, sniper calculations, ballistic corrections | Vital for accuracy at long distances, especially for ranges exceeding several kilometers |
| Aviation | Flight path corrections, navigation systems, route planning, inertial navigation, autopilot systems, long-range flights | Important for precision navigation, especially on transcontinental and transoceanic flights |
| Geophysics | Earth rotation effects, inertial navigation, GPS corrections, geodetic measurements, satellite tracking, Earth dynamics | Fundamental for geophysical understanding, accurate positioning, and Earth system science |
| Physics Education | Rotating reference frames, non-inertial frames, apparent forces, classical mechanics demonstrations, coordinate transformations | Essential for understanding dynamics, reference frames, and fictitious forces in physics |
Examples of Coriolis Effect Calculation
Real-World Applications and Use Cases
Example 1: Wind at Mid-Latitudes
Given:
- • Velocity: v = 20 m/s (wind speed)
- • Latitude: φ = 45° (mid-latitudes)
Step-by-step calculation:
Step 1: Earth's angular velocity
Ω = 7.292 × 10⁻⁵ rad/s
Step 2: Convert latitude to radians
φ = 45° = 45 × (π/180) = 0.785 rad
Step 3: Calculate Coriolis acceleration
a_c = 2vΩ sin(φ)
a_c = 2 × 20 × (7.292 × 10⁻⁵) × sin(45°)
a_c = 2 × 20 × 7.292 × 10⁻⁵ × 0.707
a_c ≈ 2.06 × 10⁻³ m/s²
Final Answer
2.06 × 10⁻³ m/s²
This small acceleration causes wind to curve to the right in the Northern Hemisphere, creating cyclonic weather patterns
Example 2: Long-Range Projectile
Given:
- • Mass: m = 50 kg
- • Velocity: v = 800 m/s
- • Latitude: φ = 60°
Step-by-step calculation:
Step 1: Calculate Coriolis acceleration
a_c = 2vΩ sin(φ)
a_c = 2 × 800 × (7.292 × 10⁻⁵) × sin(60°)
a_c = 2 × 800 × 7.292 × 10⁻⁵ × 0.866
a_c ≈ 0.101 m/s²
Step 2: Calculate Coriolis force
F_c = ma_c = 50 × 0.101
F_c ≈ 5.05 N
Final Answer
Force: 5.05 N, Acceleration: 0.101 m/s²
This Coriolis force causes significant deflection for long-range projectiles, requiring corrections in artillery and missile systems
Example 3: Ocean Current at Equator
Given:
- • Current velocity: v = 0.5 m/s
- • Latitude: φ = 0° (equator)
- • Mass of water parcel: m = 1000 kg (1 cubic meter)
Step-by-step calculation:
Step 1: Calculate Coriolis acceleration
a_c = 2vΩ sin(φ)
a_c = 2 × 0.5 × (7.292 × 10⁻⁵) × sin(0°)
a_c = 2 × 0.5 × 7.292 × 10⁻⁵ × 0
a_c = 0 m/s²
Step 2: Calculate at mid-latitudes for comparison
At φ = 45°: a_c = 2 × 0.5 × (7.292 × 10⁻⁵) × sin(45°)
a_c = 2 × 0.5 × 7.292 × 10⁻⁵ × 0.707
a_c ≈ 5.16 × 10⁻⁵ m/s²
Final Answer
At equator: 0 m/s², At 45°: 5.16 × 10⁻⁵ m/s²
The Coriolis effect is zero at the equator, explaining why ocean currents can flow directly east-west there. At mid-latitudes, even slow ocean currents experience measurable Coriolis deflection, creating the characteristic gyre circulation patterns.