Speed Calculator
Calculate speed, distance, or time using the speed formula (Speed = Distance ÷ Time). Perfect for travel planning and physics calculations.
Common Speeds
Everyday Calculators
Understanding Speed Calculations
What is Speed?
Speed is a measure of how quickly an object moves from one place to another. It is defined as the rate of change of distance with respect to time. In simple terms, speed tells us how far something travels in a given amount of time. Understanding speed is fundamental to many aspects of daily life, from driving a car to planning a trip, as well as being a cornerstone concept in physics and engineering.
The Speed Formula
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
These formulas represent the same relationship expressed in different ways, allowing you to calculate any one of the three variables when you know the other two.
Example:
- If a car travels 240 kilometers in 3 hours, its speed is 240 ÷ 3 = 80 km/h.
- If a train moves at 120 km/h for 2.5 hours, the distance covered is 120 × 2.5 = 300 kilometers.
- If a cyclist needs to cover 60 kilometers at 20 km/h, the time required is 60 ÷ 20 = 3 hours.
Common Speed Units and Conversions
Metric Units
- Kilometers per hour (km/h): Common for road speeds in most countries
- Meters per second (m/s): Standard unit in physics and scientific contexts
- Conversion: 1 m/s = 3.6 km/h or 1 km/h = 0.2778 m/s
Imperial/US Units
- Miles per hour (mph): Common for road speeds in the US and UK
- Feet per second (ft/s): Used in some engineering applications
- Conversion: 1 mph = 1.46667 ft/s or 1 ft/s = 0.681818 mph
Cross-System Conversions
- 1 mph = 1.60934 km/h
- 1 km/h = 0.621371 mph
- 1 m/s = 3.28084 ft/s
- 1 ft/s = 0.3048 m/s
- 1 knot = 1.15078 mph = 1.852 km/h
Average Speed vs. Instantaneous Speed
Average Speed
Average speed is the total distance traveled divided by the total time taken. It gives an overview of the entire journey but doesn't show variations in speed during the journey.
For example, a 240-km journey completed in 3 hours has an average speed of 80 km/h, even if the actual speed varied between 60 km/h in city sections and 100 km/h on highways.
Instantaneous Speed
Instantaneous speed is the speed of an object at a specific moment in time. It's what a car's speedometer displays—the rate of travel at that exact moment, not averaged over a journey.
In physics, instantaneous speed is calculated by finding the derivative of the distance function with respect to time, representing the speed at an infinitesimally small time interval.
Speed in Different Contexts
Travel and Transportation
- Walking: 3-5 km/h (1.8-3.1 mph)
- Bicycling: 15-30 km/h (9.3-18.6 mph)
- City driving: 30-60 km/h (18.6-37.3 mph)
- Highway driving: 80-120 km/h (49.7-74.6 mph)
- Passenger train: 80-300 km/h (49.7-186 mph)
- Commercial aircraft: 800-950 km/h (497-590 mph)
Sports
- Sprinter (100m): up to 38 km/h (23.6 mph)
- Marathon runner: 12-20 km/h (7.5-12.4 mph)
- Professional cyclist: up to 40-50 km/h (24.9-31.1 mph)
- Tennis serve: up to 250 km/h (155.3 mph)
- Golf ball: up to 270 km/h (167.8 mph)
- Formula 1 car: up to 350 km/h (217.5 mph)
Physics and Nature
- Sound in air: 343 m/s (1,235 km/h)
- Light in vacuum: 299,792,458 m/s
- Earth's rotation at equator: 1,670 km/h
- Earth's orbit around Sun: 107,000 km/h
- Solar System in galaxy: 828,000 km/h
- Hurricane winds: 119-250+ km/h
Speed-Related Concepts
Velocity vs. Speed
Speed is a Scalar
Speed is the magnitude of motion without direction. If you're traveling at 60 km/h, that's your speed regardless of which direction you're moving.
Velocity is a Vector
Velocity includes both speed and direction. Two objects moving at 60 km/h have the same speed, but if one is traveling north and the other east, they have different velocities.
In Calculations
For straight-line motion, speed and the magnitude of velocity are the same. For curved paths or direction changes, average speed and average velocity may differ significantly.
Acceleration
Definition
Acceleration is the rate of change of velocity with respect to time. It measures how quickly an object's speed or direction changes.
Formula
Acceleration = Change in Velocity ÷ Time
Units: m/s² (meters per second squared) or ft/s²
Examples
A car accelerating from 0 to 100 km/h in 8 seconds has an acceleration of 12.5 km/h/s or about 3.47 m/s².
Earth's gravitational acceleration is approximately 9.81 m/s².
Applications of Speed Calculations
Travel Planning
Calculate arrival times, estimate journey durations, and plan rest stops. For example, if you need to travel 300 km and want to arrive by 3:00 PM, starting at 9:00 AM gives you 6 hours, requiring an average speed of 50 km/h.
Fitness and Sports
Track running or cycling pace, compare performance metrics, and set training goals. For instance, a runner aiming to complete a marathon (42.195 km) in under 4 hours needs to maintain an average speed of at least 10.55 km/h.
Physics and Engineering
Design vehicles, calculate fuel efficiency, determine stopping distances, and analyze motion in various contexts. Engineers might calculate that a car traveling at 100 km/h requires approximately 80 meters to come to a complete stop.
Complex Speed Scenarios
Calculating Average Speed for Multi-Segment Journeys
When a journey consists of segments with different speeds, the overall average speed is NOT the simple average of the speeds.
For example, if you drive 100 km at 50 km/h and another 100 km at 100 km/h:
- First segment: 100 km ÷ 50 km/h = 2 hours
- Second segment: 100 km ÷ 100 km/h = 1 hour
- Total distance: 200 km
- Total time: 3 hours
- Average speed: 200 km ÷ 3 hours = 66.67 km/h
Note that this is not the simple average (75 km/h) of the two speeds.
Round Trip Average Speed
When calculating the average speed for a round trip with different speeds in each direction, the result is often surprising.
Example: If you travel to a destination at 30 km/h and return along the same route at 50 km/h:
Average Speed = 2 × (30 × 50) ÷ (30 + 50) = 2 × 1500 ÷ 80 = 3000 ÷ 80 = 37.5 km/h
The formula for round trip average speed with speeds v₁ and v₂ is:
Average Speed = 2 × (v₁ × v₂) ÷ (v₁ + v₂)
Note that this value is always less than the simple arithmetic mean of the two speeds.
Speed Across Different Fields
- Data transfer speed: Measured in bits per second (bps), kilobits per second (Kbps), megabits per second (Mbps), or gigabits per second (Gbps). A typical home internet connection might offer 100 Mbps download speed.
- Chemical reaction speed: Measured as reaction rate, typically in concentration change per time unit (mol/L·s). Affected by temperature, concentration, and catalysts.
- Processing speed: Computer processors are measured in hertz (Hz), representing clock cycles per second. Modern CPUs operate at gigahertz (GHz) speeds, typically 2-5 GHz.
- Angular speed: Measures rotational motion, expressed in radians per second (rad/s), degrees per second (°/s), or revolutions per minute (RPM). A typical car engine idles at around 800-1000 RPM.
- Wave speed: The speed at which waves propagate, such as sound waves (343 m/s in air at room temperature) or electromagnetic waves (light travels at 299,792,458 m/s in vacuum).
Speed and Safety
Speed plays a critical role in transportation safety. Higher speeds increase both the likelihood of accidents and their severity. Stopping distance increases quadratically (not linearly) with speed, meaning that a vehicle traveling at 100 km/h takes significantly more than twice the distance to stop compared to one traveling at 50 km/h. The relationship between speed and fatality risk in accidents is even more dramatic: the probability of a fatal injury in a pedestrian collision rises from about 10% at 30 km/h to over 80% at 50 km/h. This is why speed limits are set based on road design, expected hazards, and surrounding environment considerations.