Projectile Motion Calculator
Compute range, apex height, and flight time for flat-ground projectile motion (no drag). Runs locally in your browser.
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
- Input interpretation
- Enter values to calculate.
- Result
- —
- Assurance
- Engineering
- Declared partition coverage
- PASS · 2/2 declared partitions (projectile, invalid-domain) · Matrix
- Known limitations
- Flat ground; no drag; g default 9.80665
- Core CVP does not include live graph, viewport, or pointer interaction.
- Model
- Projectile range, height, flight time.
- Scope
- No drag; flat ground; constant g
- Verification
- Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
- Versions
- Calculation 1.0.0 · CVP protocol 1.0.0-proposed
- CVP identity
- 1/1 property · digest 9d01bc7ae235
- Legacy regression
- 3/3 tests · Production surface contract 4/4
- Reference
- O1 model · O2 expected_values · O2 numerical_behavior
- Interfaces
- PASS · UI (SSR) / REST / MCP
- Supplemental domain review
- Internal · Pass
- Named expert review
- Not performed
- CVP suite
- 1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
- Sources
- Classical mechanics textbooks
- ISO 80000-3 / kinematics practice
- Evidence
- 1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX physics review
- Semantic contract
- PASS
Full verification
Formulas
Core equations used by this calculator.
How to use
Enter launch speed and angle
v0 > 0; angle in degrees as labeled.
Confirm gravity if editable
Default g ≈ 9.81 m/s² unless overridden.
Read range, time of flight, and peak height
Flat-ground ideal projectile: R = v0²·sin(2θ)/g.
Example calculations
Common configurations with formula and result.
20 m/s at 45°
max range angle
Projectile Motion calculator specification
Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-09
- Engine tested 3/3 tests · Production surface contract 4/4
- Supplemental domain review Internal · Pass · 2026-08-09
- Named expert review Not performed
- Calculation version 1.0.0
Review policy · Evidence · Reviewed by CalculatorX physics review
- Definition
- R = v0² sin(2θ)/g, H = v0² sin²θ/(2g), T = 2 v0 sinθ/g on flat ground without drag.
- What it calculates
- Projectile range, height, flight time.
- Inputs
- v0_m_s
- angle_deg
- g_m_s2?
- Outputs
- range_m
- H_m
- T_s
- Formula
R=v0²sin(2θ)/g- Assumptions
- No drag; flat ground; constant g
- Units
- m/s, ° → m, s
- Boundary conditions
- angle∉(0,90) → VALUE_OUT_OF_RANGE
- Example
- v0=20 θ=45 → R≈40.79 m
- Validation cases
1 published on this page · 3/3 tests · Production surface contract 4/4 · View evidence
- v0=20 angle=45 → range≈40.7886
- Sources
- Classical mechanics textbooks — projectile motionSupports: range/apex/TOF
- ISO 80000-3 / kinematics practice — Projectile motionSupports: R = v0² sin(2θ)/g
- Classical mechanics textbooks — projectile motion
- Last reviewed
- 2026-08-09
- Reviewed by
- CalculatorX physics review
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Compute projectile motion on flat ground (no drag).
Supported and not supported
Supported — Range, apex, flight time · API physics.kinematics.projectile
Not supported — Air drag, sloping ground, Coriolis
Agent / API notes
Capability id: physics.kinematics.projectile · tool id: projectile · pin 1.0.0.
Related tools
Other calculators in this family: Force F=ma, Hz ↔ rad/s .
Frequently asked questions
Key distinctions behind the calculation.
Why not 90°?
At 90° the horizontal range is zero and the flat-ground range formula is singular for this model; API returns VALUE_OUT_OF_RANGE.