In this case we determine whether the jury instructions stating that intent to kill could be presumed from the defendant's use of a dangerous weapon, conformed to the due process standards for use of presumptions in criminal cases. We hold that the instructions did not comply with due process because they did not adequately explain the nature and operation of the presumption and did not specifically inform the jury that it was free to reject *571the presumption even if the defendant failed to present evidence rebutting the presumed fact.
On March 7, 1977, petitioner Dorothy LaVonne Savage shot and killed her husband, Daniel Savage. There were no witnesses to the fatal shooting. Petitioner was charged with first degree murder.
At trial, the prosecution's theory of the case was that Dorothy Savage committed the fatal shooting with premeditated intent to kill. In support of this theory, the prosecution presented a pathologist who testified that the nature of the wound indicated that Daniel Savage was shot in the head at close range while in a prone position. The prosecution also presented the testimony of a police officer who overheard Dorothy Savage saying to her daughter that the deceased "deserved what he got."
The defendant's evidence focused exclusively on facts supporting a theory of self-defense. Dorothy Savage testified that on the night of the killing, her husband was intoxicated, began to beat her, and produced a gun. She stated that she grabbed the gun, pulled the trigger and fired the fatal shot. She explained that she shot her husband because she thought that he was going to kill her. However, the defense did not present any evidence on the specific question of whether Mrs. Savage intended or did not intend to kill her husband when she fired in self-defense, and that fact also was not established in cross-examination.
The trial court instructed the jury on both first degree and second degree murder. The second degree murder instructions stated that the jury should find Dorothy Savage guilty of second degree murder if it concluded that "the killing not being justifiable or excusable, was done with intent to cause the death of Daniel Savage, but without premeditation." In additional instructions on the element of intent, the trial court stated:
If and when the evidence shows that one person assailed another violently with a dangerous weapon likely to kill, *572and which in fact did kill the person attacked, such evidence gives rise to a presumption that the assailant intended death or great bodily harm.
The presumption, however, may be overcome by contrary evidence, and any such evidence is sufficient to overcome it which creates in the mind of the jurors a reasonable doubt that the defendant's intent was so presumed. In the absence of evidence to the contrary, the presumption must prevail.
Instruction No. 17. Defense counsel objected to the instruction on the ground that it failed to properly state the rules governing use of presumptions.
The trial court also instructed the jury on self-defense. These instructions stated:
When a defendant claims that she killed another in self defense of her own person, the burden is upon the defendant to produce some evidence that the homicide was done in self defense. It is not necessary for the defendant to prove this to you beyond a reasonable doubt, nor by a preponderance of the evidence.
Instruction No. 21. The jury found Dorothy Savage guilty of second degree murder. Savage appealed the conviction on the basis of several claims, including the contentions that the instructions on presumption of intent from use of a dangerous weapon and the instructions on self-defense did not comply with due process requirements. The Court of Appeals affirmed the conviction. Savage then sought, and we granted, review of those parts of the Court of Appeals decision resolving the claims concerning the presumption and self-defense instructions.
I
A presumption is an evidentiary device which enables the "trier of fact to determine the existence of an element of the crime — that is, an 'ultimate' or 'elemental' fact — from the existence of one or more 'evidentiary' or 'basic' facts." County Court of Ulster County v. Allen, 442 U.S. 140, 156, 60 L. Ed. 2d 777, 791, 99 S. Ct. 2213 (1979). The use of a presumption in a particular criminal case must *573conform to several requirements which have been established to ensure that the burden always remains upon the prosecution to prove every element of the crime charged beyond a reasonable doubt. Ulster County, 442 U.S. at 155-57, 60 L. Ed. 2d at 791-92; State v. Roberts, 88 Wn.2d 337, 340, 562 P.2d 1259 (1977).
The United States Supreme Court has described several types of presumptions which vary with the strength of the requisite connection between the basic and elemental facts, and the degree to which the device restricts the fact finder's freedom to assess the evidence independently. The most restrictive type of presumption is the "conclusive" or "irre-buttable" presumption which declares that "when fact B is proven, fact A must be taken as true, and the adversary is not allowed to dispute this at all." E. Cleary, McCormick's Evidence § 342, at 804 (2d ed. 1972). Due process prohibits the use of a conclusive or irrebuttable presumption to find an element of a criminal offense, because such use of a conclusive presumption "would 'conflict with the overriding presumption of innocence with which the law endows the accused and which extends to every element of the crime,' and would 'invade [the] factfinding function' which in a criminal case the law assigns solely to the jury." Sandstrom v. Montana, 442 U.S. 510, 523, 61 L. Ed. 2d 39, 50, 99 S. Ct. 2450 (1979); Morissette v. United States, 342 U.S. 246, 274-75, 96 L. Ed. 288, 72 S. Ct. 240 (1952).
On a spectrum of presumptions ordered by the degree to which they restrict the fact finder from assessing facts independently, the next most restrictive form is the "mandatory presumption." A mandatory presumption tells the trier of fact that it must find the elemental fact upon proof of the basic fact at least unless the defendant has come forward with a certain quantum of evidence to rebut the presumed connection between the two facts. Ulster County, 442 U.S. at 157, 60 L. Ed. 2d at 792. A mandatory presumption can take any one of three different forms, depending on the degree of burden which it imposes upon the defendant in attempting to rebut the presumption. The *574first type, which has been employed in some prior cases, informs the trier of fact that, upon finding the basic fact, it must follow the presumption unless the defendant rebuts it with some quantum of evidence that is greater than "some evidence." Sandstrom v. Montana, supra at 517. Such presumptions are constitutionally deficient because they shift the "burden of persuasion" to the defendant on an element of the offense. The second type of mandatory presumption is a mandatory presumption which assigns a "strong" "burden of production" to the defendant. This form of presumption tells the "trier that he or they must find the elemental fact upon proof of the basic fact, at least unless the defendant has come forward with some evidence to rebut the presumed connection between the two facts." (Italics ours.) Ulster County, 442 U.S. at 157, 60 L. Ed. 2d at 792. Finally, the least restrictive type of "mandatory presumption" is the mandatory presumption which assigns a "weak" burden of production to the defendant. This type of presumption informs the trier that it must find the elemental fact upon proof of the basic fact, unless the defendant has come forward with "any evidence." Ulster County, 442 U.S. at 157 n.16, 60 L. Ed. 2d at 792.
The least restrictive form of presumption is the "permissive presumption," often referred to as a "permissive inference." This type of presumption "allows — but does not require — the trier of fact to infer the elemental fact from proof by the prosecutor of the basic one and . . . places no burden of any kind on the defendant." Ulster County, 442 U.S. at 157, 60 L. Ed. 2d at 792. ”[T]his permissive presumption leaves the trier of fact free to credit or reject the inference and does not shift the burden of proof . . ." Ulster County, 442 U.S. at 157, 60 L. Ed. 2d at 792.
Thus, the United States Supreme Court has described a spectrum of presumptions which range from conclusive and mandatory presumptions to permissive presumptions. As the court has explained, it is of course the function of the state courts to authoritatively define the "legal weight to be given a presumption under [state] law," within the limits of *575federal and state constitutional standards. Sandstrom v. Montana, supra at 516.
The nature of presumptions under Washington law is well established. In prior decisions, we have held that it is permissible to employ a presumption which shifts to the defendant the burden of producing "some evidence." State v. Bishop, 90 Wn.2d 185, 188-89, 580 P.2d 259 (1978); State v. Roberts, 88 Wn.2d 337, 341, 562 P.2d 1259 (1977). We have simultaneously held on the basis of the due process protections of the federal and state constitutions, that the jury must in all cases be " 'instructed that the presumption is not binding upon the jury even though the fact to be presumed is unrefuted by the defendant, and that the state must still sustain the burden of proving the defendant's guilt beyond a reasonable doubt.'" State v. Roberts, supra at 342; State v. Person, 56 Wn.2d 283, 288, 352 P.2d 189, 81 A.L.R.2d 1088 (1960); accord, State v. Bauer, 92 Wn.2d 162, 169-70, 595 P.2d 544 (1979); State v. Odom, 83 Wn.2d 541, 544-45, 520 P.2d 152 (1974). Thus, under Washington law, the trier of fact is advised that the defendant has a burden of production and, in the event the defendant fails to meet his or her burden of production, the trier should— but is not compelled to — follow the presumption.
Presumptions under Washington law can accordingly be viewed as falling partway between mandatory and permissive presumptions on the spectrum described by the United States Supreme Court. Like the mandatory presumption (and unlike the permissive presumption), a presumption under Washington law can impose upon the defendant a burden of producing "some evidence." However, unlike the mandatory presumption, the presumption under Washington law cannot compel the trier of fact to find the elemental presumed fact even in the absence of the defendant's presentation of refuting evidence.1
*576Whenever a presumption is employed in a criminal case, it is essential that the jury instructions fully and adequately explain the nature and operation of the presumption to the jury. See Sandstrom v. Montana, supra at 514-19; State v. Roberts, supra at 341. The jury instructions must, therefore, specifically inform the jury that the defendant bears no more than a burden of producing "some evidence" to rebut the presumed fact, and that the ultimate burden of proving every element of the offense beyond a reasonable doubt must always remain upon the prosecution. State v. Bishop, supra at 188-89; State v. Roberts, supra at 340-41. The jury instructions must also expressly instruct the jury that it is always free to reject the presumption even if the defendant fails to produce evidence to the contrary of the presumed fact. State v. Roberts, supra at 341-43; State v. Odom, supra at 545; State v. Person, supra at 188.
II
The petitioner contends that the instructions in this case violated the requirements for jury instructions explaining a presumption, because: (1) The instructions failed to adequately explain that the defendant bears no more than a burden of producing "some evidence," and could have been understood as shifting to the defendant an unconstitutionally great burden of persuasion on an element of the *577offense; and (2) The instructions did not explain to the jury that it could reject the presumption even if the defendant failed to produce evidence to the contrary of the presumed fact.
A
The instructions in this case stated:
If and when the evidence shows that one person assailed another violently with a dangerous weapon likely to kill, and which in fact did kill the person attacked, such evidence gives rise to a presumption that the assailant intended death or great bodily harm.
The presumption, however, may be overcome by contrary evidence, and any such evidence is sufficient to overcome it which creates in the mind of the jurors a reasonable doubt that the defendant's intent was so presumed. . . .
(Italics ours.) Instruction No. 17. The critical question, therefore, is whether the language of this instruction would have enabled a "reasonable juror" to understand that the defendant merely had to produce "some evidence" to the contrary of the presumed fact in order to rebut the presumption.
In State v. Kroll, 87 Wn.2d 829, 558 P.2d 173 (1976), we considered a jury instruction which similarly established a presumption with respect to an element of the offense, and imposed upon the defendant "the burden of creating a reasonable doubt" as to the validity of the presumed fact. Kroll, at 839 n.3. We held in Kroll that an instruction of this type shifts an unconstitutionally great burden of proof to the defendant. Subsequently, in State v. Roberts, supra at 345, and State v. Hanton, 94 Wn.2d 129, 614 P.2d 1280 (1980), we reaffirmed, this principle and held that jury instructions which impose upon the defendant "the burden of creating a reasonable doubt in the mind of the jurors" shift an unconstitutionally great burden to the defendant.
The jury instructions in the present case therefore resulted in an unconstitutional shifting of the burden of persuasion to the defendant. A reasonable juror may well *578have believed that the defendant's burden of creating a reasonable doubt in the minds of the jurors represented a quantum of evidence that was greater than the burden of simply producing "some evidence."
The instructions in this case were particularly likely to result in juror misunderstanding of the defendant's burden because different terminology was employed in the various instructions to define the defendant's burden of production. In the instructions on the presumption of intent to kill from attack with a dangerous weapon, the jurors were told that the defendant could rebut the presumption by presenting evidence sufficient to raise a reasonable doubt as to the validity of the presumed fact. In contrast, the self-defense instructions properly informed the jury that with respect to self-defense, the defendant merely had to "produce some evidence." In an area of law that is as complex as presumptions and burdens of proof, it is essential that the jury instructions facilitate juror understanding by employing, whenever possible, uniform terminology to describe the defendant's burden of production.
It remains to be determined whether the error in this case was prejudicial or harmless error. Since the error infringed upon a constitutional right of the petitioner, the error is presumed to be prejudicial, and the State has the burden of proving that the error was harmless. State v. Stephens, 93 Wn.2d 186, 190-91, 607 P.2d 304 (1980); see Chapman v. California, 386 U.S. 18, 23-24, 17 L. Ed. 2d 705, 87 S. Ct. 824, 24 A.L.R.3d 1065 (1967). The constitutional error cannot be declared harmless unless it was '"harmless beyond a reasonable doubt."' State v. Stephens, supra at 191. An error in instructions is harmless if it is "trivial, or formal, or merely academic, and was not prejudicial to the substantial rights of the party assigning it, and in no way affected the final outcome of the case." State v. Wanrow, 88 Wn.2d 221, 237, 559 P.2d 548 (1977); State v. Golladay, 78 Wn.2d 121, 139, 470 P.2d 191 (1970).
In this case, it cannot be concluded beyond a reasonable *579doubt that the error did not in any way affect the final outcome of the case. The prosecution's evidence of intent to kill was entirely circumstantial and would not in and of itself have certainly led to the conclusion that Dorothy Savage intended to kill her husband when she fired the fatal shot. The evidence was, however, sufficient to show that Dorothy Savage "assailed another violently with a dangerous weapon likely to kill,” and therefore the presumption of intent to kill would have come into effect. As a result of the error in the instructions, the jurors could well have misunderstood the amount of evidence that the defendant had to present in order to rebut this presumption. A reasonable juror could have been led to mistakenly believe that the defendant had the burden of presenting some quantum of evidence that was greater than "some evidence" in order to rebut the presumed connection between the basic fact of an attack with a dangerous weapon and the elemental fact of intent to kill. See State v. Hanton, supra at 134; State v. Roberts, supra at 345. The defendant's evidence showing that she fired spontaneously in self-defense could conceivably have been considered by the jury as "some evidence" rebutting the presumed connection between her use of the gun and an intent to kill. But, because the defendant did not present any evidence explicitly denying intent to kill, a reasonable juror may not have considered the defendant's evidence sufficient to satisfy a burden of rebuttal that was greater than the burden of producing "some evidence." Accordingly, a reasonable juror would have mistakenly concluded that the defendant had not met her burden of rebuttal, and that the presumption of intent to kill should be followed. The finding of intent to kill and the conviction of second degree murder would than have been based on the erroneous instructions concerning the operation of the presumption.
The error must, therefore, be deemed prejudicial. The conviction must be reversed and the case remanded for a new trial with proper jury instructions.
*580B
There is an additional and independent reason for reversing this conviction and remanding for a new trial. The presumption instructions in this case also violated the requirement that the jury be informed that it is not bound by the presumption even in the absence of evidence to the contrary of the presumed fact.
In State v. Person, 56 Wn.2d 283, 352 P.2d 189, 81 A.L.R.2d 1088 (1960), we explained that when a jury is instructed regarding a presumption,
the jury should be . . . instructed that the presumption is not binding upon the jury even though the fact to be presumed is unrefuted by the defendant, and that the state must still sustain the burden of proving the defendant's guilt beyond a reasonable doubt. In other words, it should be made clear that the statutory presumption permits, but in no way directs, the jury to convict the accused, and must be considered by the jury in the light of the presumption of innocence which arises upon a plea of not guilty . . .
State v. Person, supra at 288. This requirement, which is based on the due process guaranties of the federal and state constitutions, has been repeatedly reaffirmed. See, e.g., State v. Thomas, 58 Wn.2d 746, 749-50, 364 P.2d 930 (1961); State v. Odom, 83 Wn.2d 541, 544-45, 520 P.2d 152 (1974); State v. Roberts, 88 Wn.2d 337, 340, 562 P.2d 1259 (1977).
In the present case, the trial court instructed the jury that "[i]n the absence of evidence to the contrary [of the presumed fact], the presumption must prevail." Thus, the instructions directly violated the requirement that the jury be informed that even in the absence of evidence to the contrary of the presumed fact, it is nevertheless free to choose to reject the presumption.
This error was also prejudicial. The defendant in this case did not present any evidence specifically addressing the question of intent to kill. Thus, although it is possible that the jury considered the defendant's evidence to be "some evidence" rebutting the presumed connection *581between the basic and elemental facts, it is equally possible that the jury would have concluded that there was no evidence to the contrary of the presumed fact. The jury would then have erroneously felt itself bound by the presumption of intent to kill. Accordingly, it cannot be concluded beyond a reasonable doubt that the error "in no way affected the final outcome of the case." State v. Wanrow, supra at 237.
Ill
The petitioner's final contention is that the instructions on self-defense were constitutionally inadequate in that they did not specifically state that the prosecution bears the burden of proving absence of self-defense.
The instruction in this case defined the crime of second degree murder in the following manner:
To constitute the crime of Murder in the Second Degree in the case before you, it will be necessary for the State to satisfy you beyond a reasonable doubt of the truth of each of the following elements:
1. That Daniel Savage was killed on or about the 7th day of March, 1977;
2. That the killing was done by Dorothy LaVonne Savage, the defendant;
3. That the killing took place in Pierce County, Washington;
4. That the killing not being justifiable or excusable, was done with intent to cause the death of Daniel Savage, but without premeditation;
(Italics ours.) Instruction No. 6. The instructions then further defined "justifiable homicide":
The killing of a human being is justifiable when committed in the lawful defense of the slayer when there is reasonable ground to apprehend a design on the part of the person slain to commit a felony or to do some great personal injury to the slayer and there is imminent danger of such design being accomplished. One attacked has the right to repel force with force, but the use of excessive force by the slayer does not excuse or justify a homicide.
Instruction No. 20.
*582In State v. King, 92 Wn.2d 541, 599 P.2d 522 (1979), the defendant was convicted of second degree murder on the basis of essentially identical jury instructions. The defendant in King claimed that the State bears the burden of proving absence of self-defense in second degree murder cases, and the jury must be explicitly instructed to this effect. We held that it was unnecessary to reach the question of whether the State bore such a burden with respect to second degree murder for, even assuming arguendo that the State did bear such a burden, the jury instructions sufficiently allowed the defendant to argue his theory of the case. We explained that the instructions defining second degree murder as a killing that was not "justifiable" allowed the defendant to argue to the jury that the State bore the burden of proving absence of self-defense. Thus, even assuming arguendo that the State had such a burden, it was not necessary to explicitly instruct on that burden. State v. King, supra at 546.
In the present case, petitioner similarly argues that the State bears the burden of proving absence of self-defense and that the jury must be explicitly instructed to this effect. Like the instructions in King, the instructions in this case stated that second degree murder is a killing that is not "justifiable." Thus, even assuming for the sake of argument that the State has such a burden with respect to second degree murder, the petitioner would not have been prejudiced by the failure to explicitly instruct on this burden.
Therefore, the petitioner's contention concerning the self-defense instruction is without merit.
IV
The presumption instructions in this case were constitutionally deficient in that they failed to properly define the defendant's burden of production and failed to inform the jury that it was not bound by the presumption even in the absence of evidence refuting the presumed fact.
*583Therefore, the conviction is reversed and the case is remanded for a new trial.
Stafford, Horowitz, and Williams, JJ., concur.
One of the ramifications of this “semi-mandatory" nature of the Washington presumption is that "a presumption may only be used to establish an element of a criminal oifense when it is established that the fact presumed follows from the *576facts proven in support thereof beyond a reasonable doubt." State v. Roberts, 88 Wn.2d 337, 341, 562 P.2d 1259 (1977); State v. Alcantara, 87 Wn.2d 393, 397-98, 552 P.2d 1049 (1976); State v. Odom, 83 Wn.2d 541, 548, 520 P.2d 152 (1974). The degree of connection that must exist between a fact presumed and the facts proven is determined by the nature of the presumption and the extent to which the presumption restricts the fact finder from assessing the evidence independently. See County Court of Ulster County v. Allen, 442 U.S. 140, 159-60,165-67, 60 L. Ed. 2d 777, 793-94, 797-98, 99 S. Ct. 2213 (1979). Thus, a "mandatory presumption" requires a "beyond a reasonable doubt" connection between the presumed fact and the proven facts, whereas a "permissive presumption" requires merely a "more likely than not" connection between these facts. Ulster County, 442 U.S. at 166, 60 L. Ed. 2d at 797-98. The semi-mandatory Washington presumption restricts the fact finder to a certain extent and therefore it is necessary to establish that the fact presumed follows "beyond a reasonable doubt" from the facts proven in support thereof.