Moon Phase worksheet

1. Moon phase: Waxing Gibbous

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Apr 27, 2026}\text{12:00 UTC}$$=\text{JD}\mathrm{2,461,158}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Apr 17, 2026, 11:54 UTC}\text{(JD}\mathrm{2,461,147.9959}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,461,158}-\mathrm{2,461,147.9959}$$=10\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}48.37\text{°}}{2}$$=0.8321\times 100$$=\mathrm{83.2\%}$

5. The last main phase was a new moon, so the lit part is growing (waxing). Under 50% lit is a crescent, and over 50% is gibbous

   $\text{phase}$$=\text{Waxing Gibbous}$

2. Moon phase: Waxing Gibbous

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Dec 13, 2024}\text{12:00 UTC}$$=\text{JD}\mathrm{2,460,658}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Dec 1, 2024, 06:23 UTC}\text{(JD}\mathrm{2,460,645.7662}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,460,658}-\mathrm{2,460,645.7662}$$=12.23\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}24.95\text{°}}{2}$$=0.9533\times 100$$=\mathrm{95.3\%}$

5. The last main phase was a new moon, so the lit part is growing (waxing). Under 50% lit is a crescent, and over 50% is gibbous

   $\text{phase}$$=\text{Waxing Gibbous}$

3. Moon phase: Waning Gibbous

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Feb 6, 2026}\text{12:00 UTC}$$=\text{JD}\mathrm{2,461,078}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Jan 18, 2026, 19:54 UTC}\text{(JD}\mathrm{2,461,059.3291}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,461,078}-\mathrm{2,461,059.3291}$$=18.67\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}303.71\text{°}}{2}$$=0.7775\times 100$$=\mathrm{77.8\%}$

5. The last main phase was a full moon, so the lit part is shrinking (waning). Over 50% lit is gibbous, and under 50% is a crescent

   $\text{phase}$$=\text{Waning Gibbous}$

4. Moon phase: Waning Crescent

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Feb 4, 2027}\text{12:00 UTC}$$=\text{JD}\mathrm{2,461,441}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Jan 7, 2027, 20:26 UTC}\text{(JD}\mathrm{2,461,413.3514}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,461,441}-\mathrm{2,461,413.3514}$$=27.65\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}203.72\text{°}}{2}$$=0.0422\times 100$$=\mathrm{4.2\%}$

5. The last main phase was a full moon, so the lit part is shrinking (waning). Over 50% lit is gibbous, and under 50% is a crescent

   $\text{phase}$$=\text{Waning Crescent}$

5. Moon phase: Waning Gibbous

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Jan 25, 2027}\text{12:00 UTC}$$=\text{JD}\mathrm{2,461,431}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Jan 7, 2027, 20:26 UTC}\text{(JD}\mathrm{2,461,413.3514}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,461,431}-\mathrm{2,461,413.3514}$$=17.65\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}318.88\text{°}}{2}$$=0.8767\times 100$$=\mathrm{87.7\%}$

5. The last main phase was a full moon, so the lit part is shrinking (waning). Over 50% lit is gibbous, and under 50% is a crescent

   $\text{phase}$$=\text{Waning Gibbous}$

6. Moon phase: New Moon

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Jul 24, 2025}\text{12:00 UTC}$$=\text{JD}\mathrm{2,460,881}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Jun 25, 2025, 10:33 UTC}\text{(JD}\mathrm{2,460,851.9398}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,460,881}-\mathrm{2,460,851.9398}$$=29.06\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}184.09\text{°}}{2}$$=0.0013\times 100$$=\mathrm{0.1\%}$

5. The exact new moon falls on this UTC date (19:13 UTC), so the day is named after it

   $\text{phase}$$=\text{New Moon}$

7. Moon phase: Waning Crescent

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Apr 15, 2026}\text{12:00 UTC}$$=\text{JD}\mathrm{2,461,146}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Mar 19, 2026, 01:26 UTC}\text{(JD}\mathrm{2,461,118.5595}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,461,146}-\mathrm{2,461,118.5595}$$=27.44\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}206.6\text{°}}{2}$$=0.0529\times 100$$=\mathrm{5.3\%}$

5. The last main phase was a full moon, so the lit part is shrinking (waning). Over 50% lit is gibbous, and under 50% is a crescent

   $\text{phase}$$=\text{Waning Crescent}$

8. Moon phase: Waning Crescent

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Jul 11, 2026}\text{12:00 UTC}$$=\text{JD}\mathrm{2,461,233}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Jun 15, 2026, 02:56 UTC}\text{(JD}\mathrm{2,461,206.6224}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,461,233}-\mathrm{2,461,206.6224}$$=26.38\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}221.14\text{°}}{2}$$=0.1234\times 100$$=\mathrm{12.3\%}$

5. The last main phase was a full moon, so the lit part is shrinking (waning). Over 50% lit is gibbous, and under 50% is a crescent

   $\text{phase}$$=\text{Waning Crescent}$

9. Moon phase: Waning Crescent

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Nov 17, 2025}\text{12:00 UTC}$$=\text{JD}\mathrm{2,460,997}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Oct 21, 2025, 12:26 UTC}\text{(JD}\mathrm{2,460,970.0183}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,460,997}-\mathrm{2,460,970.0183}$$=26.98\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}210.22\text{°}}{2}$$=0.068\times 100$$=\mathrm{6.8\%}$

5. The last main phase was a full moon, so the lit part is shrinking (waning). Over 50% lit is gibbous, and under 50% is a crescent

   $\text{phase}$$=\text{Waning Crescent}$

10. Moon phase: Waxing Gibbous

1. Turn the date (at 12:00 UTC) into a Julian day (JD), the running day count astronomers use, so dates are easy to subtract

   $\text{Feb 15, 2027}\text{12:00 UTC}$$=\text{JD}\mathrm{2,461,452}$

2. Find the last true new moon. Start from the average cycle of 29.530589 days, then correct for the Moon's and Earth's oval orbits

   $\text{previous new moon}$$=\text{Feb 6, 2027, 15:58 UTC}\text{(JD}\mathrm{2,461,443.1651}\text{)}$

3. The moon's age is the time since that new moon

   $\mathrm{2,461,452}-\mathrm{2,461,443.1651}$$=8.83\text{\hspace{0.17em}days}$

4. Find how much of the moon is lit. It depends on the angle i at the Moon between the Sun and Earth. That angle comes mainly from how far apart the Moon and Sun look in the sky

   $\frac{1+\text{cos}74.71\text{°}}{2}$$=0.6318\times 100$$=\mathrm{63.2\%}$

5. The last main phase was a new moon, so the lit part is growing (waxing). Under 50% lit is a crescent, and over 50% is gibbous

   $\text{phase}$$=\text{Waxing Gibbous}$